References
Published online by Cambridge University Press: 05 January 2015
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Supersymmetric Field TheoriesGeometric Structures and Dualities, pp. 394 - 407Publisher: Cambridge University PressPrint publication year: 2015
References
[1] , and 1982. Stability of gravity with a cosmological constant. Nucl. Phys., B195, 76.CrossRefGoogle Scholar
[3] , , , and 2008. N = 6 superconformal Chern–Simons–matter theories, M2-branes and their gravity duals. JHEP, 0810, 091.CrossRef
[4] 1990. Homogeneous complex manifolds. Pages 148–244. of: Several Complex Variables IV. (Encyclopaedia of Mathematical Sciences, vol. 10). Springer.CrossRefGoogle Scholar
[5] 1975. Classification of quaternionic spaces with transitive solvable group of motion. Ozv. Akad. Nauk. SSSR Ser. Math., 39, 315–362.Google Scholar
[6] , , and 1998. Lie group valued momentum maps. J. Differential Geom., 48, 445–195.CrossRefGoogle Scholar
[7] 1983. Supersymmetry and the Atiyah–Singer index theorem. Commun. Math. Phys., 90, 161–173.CrossRefGoogle Scholar
[8] , and 1983. Potentials for the supersymmetric non–linear σ-models. Commun. Math. Phys., 91, 87.CrossRefGoogle Scholar
[9] , and 1980. Kähler geometry and the renormalization of supersymmetric sigma models. Phys. Rev., D22, 846.Google Scholar
[10] , and 1981. Geometrical structure and ultraviolet finiteness in the supersymmetric sigma model. Commun. Math. Phys., 80, 443.CrossRefGoogle Scholar
[12] , , and 1981. The background field method and the ultraviolet structure of the supersymmetric nonlinear sigma model. Ann. Phys., 134, 85.CrossRefGoogle Scholar
[14] , , , , , , and 1997. N =2 supergravity and N = 2 superYang–Mills theory on general scalar manifolds: symplectic covariance, gaugings and the momentum map. J. Geom. Phys., 23, 111–189.CrossRefGoogle Scholar
[15] , , , and 2001. Nonsemisimple gaugings of D = 5 N = 8 supergravity and FDA.s. Class. Quant. Grav., 18, 395–414.CrossRefGoogle Scholar
[16] , , , and 2002a. Duality and spontaneously broken supergravity in flat backgrounds. Nucl. Phys., B640, 63–77.Google Scholar
[17] , , , and 2002b. Gauging of flat groups in four-dimensional supergravity. JHEP, 0207, 010.CrossRefGoogle Scholar
[18] 1989. Mathematical Methods of Classical Mechanics. (Graduate Texts in Mathematics, vol. 60). Springer.CrossRefGoogle Scholar
[19] , and 2001. Symplectic geometry. In: Dynamical Systems. IV. (Encyclopaedia of Mathematical Sciences, vol. 4). Springer.CrossRefGoogle Scholar
[20] 1988a. Collected Works. Vol. 3. Index Theory. Oxford Science Publications; Oxford University Press.Google Scholar
[21] 1988b. Collected Works. Vol. 4. Index Theory: 2. Oxford Science Publications; Oxford University Press.Google Scholar
[22] 1984. The momentum map in symplectic geometry. Pages 43–51. of: Durham Symposium on Global Riemannian Geometry. Ellis Horwood Ltd.Google Scholar
[23] , and 1966. A Lefschetz fixed point formula for elliptic differential operators. Bull. Amer. Math. Soc., 12, 245.CrossRefGoogle Scholar
[24] , and 1982. Yang–Mills equations over Riemann surfaces. Phil. Trans. R. Soc. Lond., A308, 523–615.Google Scholar
[25] , and 1984. The momentum map and equivariant cohomology. Topology, 23, 1–28.CrossRefGoogle Scholar
[27] , and 1986. Gauged N = 4, d = 6 Maxwell–Einstein supergravity and “antisymmetric-tensor Chern–Simons” forms. Phys. Rev., D33(Mar), 1557–1562.Google Scholar
[30] , and 2008. Gauge symmetry and supersymmetry of multiple M2-branes. Phys. Rev., D77, 065008.Google Scholar
[31] , and 1983. Matter couplings in N = 2 supergravity. Nucl. Phys., B222, 1.CrossRefGoogle Scholar
[32] , and 2011. Symmetries and strings in field theory and gravity. Phys. Rev., D83, 084019.Google Scholar
[33] 1993. Real Killing spinors and holonomy. Commun. Math. Phys., 154, 509–521.CrossRefGoogle Scholar
[34] 2002. Conformal Killing spinors and special geometric structures in Lorentzian geometry – a survey. arXiv:math/0202008 [math.DG].
[35] 2008. Conformal Killing spinors and the holonomy problem in Lorentzian geometry – A survey of new results. In: Symmetries and Overdetermined Systems of Partial Differential Equations. Springer.Google Scholar
[36] 2011. Holonomy groups of Lorentzian manifolds – a status report. Available at the author's webpage: http://www.mathematik.hu-berlin.de/baum/publikationen-fr/Publikationen-ps-dvi/Baum-Holono-my-report-final.pdf. Accessed August 13, 2014.
[37] , and 1999. Parallel spinors and holonomy groups on pseudo'Riemannian spin manifolds. Ann. Global Anal. Geom., 17, 1–17.CrossRefGoogle Scholar
[38] , , , and 1991. Twistor and Killing Spinors on Riemannian Manifolds. (Teubner–Texte zur Mathematik, vol. 124). Teubner-Verlag.Google Scholar
[39] , and 1993. On the holonomy of Lorentzian manifolds. In: Differential Geometry: Geometry in Mathematical Physics and Related Topics. American Mathematical Society.Google Scholar
[40] , , and 2003. Calabi–Yau fourfolds with flux and supersymmetry breaking. JHEP, 04, 3–38.Google Scholar
[41] 1955. Sur les groupes d'holonomie des variétés à connexion affine et des variétés riemanniennes. Bull. Soc. Math. France., 83, 279–330.Google Scholar
[43] , , and 1971. Le spectre d'une varieté riemannienne. (Lectures Notes in Mathematics, vol. 194). Springer.CrossRefGoogle Scholar
[44] 1950. The Kernel Function and Conformal Mapping. (Mathematical Surveys and Monographs, vol. 5). America Mathematical Society.CrossRefGoogle Scholar
[45] , , and 1985. Coupling YangéMills to N = 4 d = 4 supergravity. Phys. Lett., B155, 71–75.Google Scholar
[46] , , , and 2010. Superconformal sigma models in three dimensions. Nucl. Phys., B838, 266–297.Google Scholar
[47] , , and 2008a. Multiple M2-branes and the embedding tensor. Class. Quant. Grav., 25, 142001.CrossRefGoogle Scholar
[48] , , , , and 2008b. The superconformal gaugings in three dimensions. JHEP, 0809, 101.CrossRefGoogle Scholar
[49] 2001. An Introduction to Symplectic Geometry. (Graduate Studies in Mathematics, vol. 26). American Mathematical Society.Google Scholar
[50] , , , and 1994. Kodaira–Spencer theory of gravity and exact results for quantum string amplitudes. Commun. Math. Phys., 165, 311–428.CrossRefGoogle Scholar
[53] , and 1995. Localization and diagonalization: a review of functional integral techniques for low-dimensional gauge theories and topological field theories. J. Math. Phys., 36, 2192–2236.CrossRefGoogle Scholar
[54] , and 1988. Supermembranes and the signature of space-time. Nucl. Phys., B310, 387–404.Google Scholar
[55] 1949. Some remarks about Lie groups transitive on spheres and tori. Bull. Amer. Math. Soc., 55, 580–587.CrossRefGoogle Scholar
[56] 1950. Le plan projectif des octaves et les sphéres comme espaces homogènes. C. R. Acad. Sci. Paris, 230, 1378–1380.Google Scholar
[57] 1960. On the curvature tensor of Hermitian symmetric manifolds. Ann. Math., 71, 508–521.CrossRefGoogle Scholar
[60] , and 1982. Differential Forms in Algebraic Topology. (Graduate Texts in Mathematics, vol. 82). Springer.CrossRefGoogle Scholar
[61] 1989. Elements of Mathematics. Lie Groups and Lie Algebras. Chapt. 1–3. Springer.Google Scholar
[62] , and 2008. Sasakian Geometry. (Oxford Mathematical Monographs). Oxford University Press.Google Scholar
[64] , , and 1993. Quaternionic reduction and Einstein manifolds. Commun. Anal. Geom., 1, 229–279.CrossRefGoogle Scholar
[65] , and 1985. Representations of Compact Lie Groups. (Graduate Texts in Mathematics vol. 98). Springer.CrossRefGoogle Scholar
[66] , and 1983. Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle. Pages 77–102. of: and (eds.), Arithmetic and Geometry. Papers dedicated to I.R. Shafarevich. Vol. II. Birkhäuser.Google Scholar
[67] , , , , and 1991. Exterior Differential Systems. (Mathematical Sciences Research Institute Publications, vol. 18). Springer.
[68] 1997. Automorphic Forms and Representations. (Studies in Advanced Mathematics, vol. 55). Cambridge University Press.CrossRefGoogle Scholar
[71] , and 1960. On compact, locally symmetric Kahler manifolds. Ann. Math., 71, 472–507.CrossRefGoogle Scholar
[72] , and 1984. N =2, d = 2 nonchiral supergravity and its spontaneous compactification. Nucl. Phys., B243, 112–124.Google Scholar
[73] 1988. Yukawa couplings between (2,1) forms. Nucl. Phys., B298, 458.
[74] , , , and 1985. Vacuum configurations for superstrings. Nucl. Phys., B 258, 46–74.Google Scholar
[75] , , , and 1991. A pair of Calabi–Yau manifolds as an exactly soluble superconformal theory. Nucl. Phys., B 359, 21–74.Google Scholar
[76] 2008. Lectures on Symplectic Geometry. (Lecture Notes in Mathematics, vol. 1764). Springer.CrossRefGoogle Scholar
[77] , , and 2003. Period Mappings and Period Domains. (Cambridge Studies in Advanced Mathematics, vol. 85). Cambridge University Press.Google Scholar
[78] 1935. Sur les domaines bornés homogènes de l'espace de n variables complexes. Abh. Math. Semin. Univ. Hamb., 11, 116–162.CrossRefGoogle Scholar
[79] , , , , , and 1985. σ Models, duality transformations and scalar potentials in extended supergravities. Phys. Lett., B161, 91.CrossRefGoogle Scholar
[80] , , , , , and 1986a. The complete N = 3 matter coupled supergravity. Nucl. Phys., B268, 376–382.Google Scholar
[81] , , , , , and 1986b. The complete N = 3 matter coupled supergravity. Nucl. Phys., B268, 317.CrossRefGoogle Scholar
[82] , , and 1991. Supergravity and Superstrings: A Geometrical Perspective, vols. 1, 2 … 3. World Scientific.CrossRefGoogle Scholar
[83] 1988. Homogeneous Kähler manifolds and flat potential N = 1 supergravities. Phys. Lett., B215, 489–490.Google Scholar
[84] 1989. Homogeneous Kähler manifolds and T algebras in N = 2 super-gravity and superstrings. Commun. Math. Phys., 124, 23–55.CrossRefGoogle Scholar
[86] , and 1982. Functional measure, topology and dynamical supersymmetry breaking. Phys. Lett., B110, 39.CrossRefGoogle Scholar
[88] (ed.). 1985. John Hopkins workshop on current problems in particle theory 9: new trends in particle theory. Singapore: World Scientific.
[90] , , and 1988. Hidden noncompact symmetries in string theories. Nucl. Phys., B308, 436.CrossRefGoogle Scholar
[91] , , and 1989. Geometry of type II superstrings and the moduli of superconformal field theories. Int. J. Mod. Phys., A4, 2475.CrossRefGoogle Scholar
[92] , and 1983. Unification of Yang–Mills theory and super-gravity in ten dimensions. Phys. Lett., B120, 124–134.Google Scholar
[93] 1943. On the Curvatura Integra in a Riemannian manifold. Ann. Math., 46, 674–684.Google Scholar
[94] 1979. Complex Manifolds without Potential Theory (with an Appendix in the Geometry of Characteristic Classes). Springer.CrossRefGoogle Scholar
[95] , , , , , , , , and 2007. The Ricci Flow: Techniques and Applications. Part I: Geometric Aspects. (Mathematical Surveys and Monographs vol. 135). American Mathematical Society.Google Scholar
[96] , and 1967. All possible symmetries of the S-matrix. Phys. Rev., 159, 1251.CrossRefGoogle Scholar
[97] , , , , and 1998. N = 8 gaugings revisited: an exhaustive classification. Nucl. Phys., B532, 245–279.Google Scholar
[99] , and 1985. Classification of Kähler manifolds in N = 2 vector multiplet supergravity couplings. Class. Quant. Grav., 2, 445.CrossRefGoogle Scholar
[100] , , , , , and 1979. Spontaneous symmetry breaking and Higgs effect in supergravity without cosmological constant. Nucl. Phys., B147, 105.CrossRefGoogle Scholar
[101] , , , and 1983a. Naturally vanishing cosmological constant in N = 1 supergravity. Phys. Lett., B133, 61.CrossRefGoogle Scholar
[102] , , , and 1983b. Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect. Nucl. Phys., B212, 413.CrossRefGoogle Scholar
[103] , , , and 2009. The chiral ring of AdS3/CFT and the atractor mechanism. JHEP, 0903, 030.CrossRefGoogle Scholar
[105] , , de , and 1980. Chiral super-fields in N = 2 supergravity. Nucl. Phys., B173, 175.CrossRefGoogle Scholar
[107] 1982. Conformal invariance in extended supergravity. Pages 267–312. of: Supergravity 1981. Cambridge University Press.Google Scholar
[108] 2002. Supergravity. Lectures at the 2001 Le Houches Summer School. arXiv:hep-th/0212245.
[111] , and 2005. Gauged maximal supergravities and hierarchies of nonabelian vector—tensor systems. Fortsch. Phys., 53, 442–449.CrossRefGoogle Scholar
[113] , and 1989. Rigidly and locally supersymmetric two-dimensional non-linear σ-models with torsion. Nucl. Phys., B2, 58–94.Google Scholar
[114] de , and 1984. Potentials and symmetries of general gauged N = 2 supergravity–Yang–Mills models. Nucl. Phys., B245, 89–117.Google Scholar
[115] de , and 1992. Special geometry, cubic polynomials and homogeneous quaternionic spaces. Commun. Math. Phys., 149, 307–334.Google Scholar
[117] , , , , and 1984. Gauge and matter fields coupled to N = 2 supergravity. Phys. Lett., B134, 37.CrossRefGoogle Scholar
[118] , , and 1985. Lagrangians of N = 2 super-gravity – matter systems. Nucl. Phys., B255, 569.CrossRefGoogle Scholar
[119] de , , and 1993. Locally supersymmetric D = 3 nonlinear sigma models. Nucl. Phys., B 392, 3–38.Google Scholar
[120] , , and 2003a. Gauged locally supersymmetric D = 3 nonlinear sigma models. Nucl. Phys., B671, 175–216.Google Scholar
[121] , , and 2003b. On Lagrangians and gaugings of maximal supergravities. Nucl. Phys., B655, 93–126.Google Scholar
[122] , , and 2004. Gauging maximal supergravities. Fortsch. Phys., 52, 489–496.CrossRefGoogle Scholar
[123] , , and 2008. Gauged supergravities, tensor hierarchies, and M-theory. JHEP, 0802, 044.CrossRefGoogle Scholar
[124] 2008. Les Houches Lectures on Constructing String Vacua. e-print arXiv:0803.1194.
[126] , , and 1982. Topologically massive gauge theories. Ann. Phys., 140, 373–411.CrossRefGoogle Scholar
[128] 1931. Quantised singularities in the electromagnetic field. Proc. R. Soc., A133, 60–73.Google Scholar
[129] , and 1996. Supersymmetric Yang–Mills theory and integrable systems. Nucl. Phys., B460, 299–334.Google Scholar
[130] , and (eds.). 2008. From Hodge Theory to Integrability and TQFT: tt*-geometry. American Mathematical Society.
[131] , and 1982. On the variation in the cohomology in the symplectic form of the reduced phase space. Invent. Math., 69, 259–268.CrossRefGoogle Scholar
[132] , and 2011. Supercurrents and brane currents in diverse dimensions. JHEP, 1107, 095.CrossRefGoogle Scholar
[135] , and 1986. Integrability of the principal chiral field model in (1+1)-dimension. Ann. Phys., 167, 227.CrossRefGoogle Scholar
[136] , and 1992. Riemann Surfaces. (Graduate Texts in Mathematics, vol. 71). Springer.CrossRefGoogle Scholar
[137] , and 2012. LieART – A Mathematical application for Lie algebras and Representation Theory. arXiv:1206.6379 [math-ph].
[138] , and 1990. Quaternionic manifolds for type II superstring vacua of Calabi–Yau spaces. Nucl. Phys., B 332, 317–332.Google Scholar
[139] , and 1982. Representations of extended supersymmetry on one and two-particle states. Pages 47–84.of: Supergravity 1981. Cambridge University Press.Google Scholar
[140] , and 1989. A theorem on N = 2 special Kahler product manifolds. Class. Quant. Grav., 6, L243.CrossRefGoogle Scholar
[141] , , and 1997. Supersymmetry and the cohomology of (hyper) Kahler manifolds. Nucl. Phys., B503, 614–626.Google Scholar
[142] , , and 2004. Nonsemisimple and complex gaugings of N = 16 supergravity. Commun. Math. Phys., 249, 475–496.CrossRefGoogle Scholar
[143] 1995. Symplectic Geometry. 2nd ed. (Advanced Studies in Contemporary Mathematics, vol. 5). Gordon and Breach.Google Scholar
[147] , , and 1976. Progress toward a theory of supergravity. Phys. Rev., D13, 3214–3218.Google Scholar
[148] 1988. Introduction to Supersymmetry. Cambridge Monographs on Mathematical Physics. Cambridge University Press.Google Scholar
[149] , and 2002. From holomorphic functions to complex manifolds. Graduate Texts in Mathematics, vol. 213. Springer.CrossRefGoogle Scholar
[150] , and 1981. Duality rotations for interacting fields. Nucl. Phys., B193, 221–244.Google Scholar
[151] , and 2010. Janus configurations, Chern-Simons couplings, and the theta-angle in N=4 Super Yang-Mills Theory. JHEP, 1006, 097.CrossRefGoogle Scholar
[152] , and 2007. Notes on superconformal Chern-Simons-Matter theories. JHEP, 0708, 056.CrossRefGoogle Scholar
[153] 2006. Isometry groups of Lobachewskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups. Rend. Circ. Mat. Palermo, 79, 87–97.Google Scholar
[154] and 1988. Quaternionic reduction and quaternionic orbifolds. Math. Ann., 282, 1–21.CrossRefGoogle Scholar
[155] 1987. A generalization of the momentum mapping construction for quaternionic Kahler manifolds. Commun. Math. Phys., 108, 117–138.CrossRefGoogle Scholar
[156] Volume of SL(n, ℤ)\SL(n,ℝ) and Spn(ℤ)\Spn(ℝ). Available at http://www.users.math.umn.edu/∼garrett/m/v/volumes.pdf. Accessed August 13, 2014.
[157] , , , and 2001. Superspace, or One Thousand and One Lessons in Supersymmetry. Free electronic version of the 1983 book (with corrections). Availableas arXiv:hep-th/0108200.Google Scholar
[159] , and 1982. A Bogomolny bound for general relativity and solitons in N = 2 supergravity. Phys. Lett., B 109, 190.CrossRefGoogle Scholar
[160] , , and 1983. The stability of gauged super-gravity. Nucl. Phys., B218, 173.CrossRefGoogle Scholar
[161] , and 1965. Classification and canonical realization of complex bounded homogeneous domains. Pages 404–437. of: Transactions of the Moscow Mathematical Society for the Year 1963. American Mathematical Society.Google Scholar
[162] , , and 1994. Target space duality in string theory. Phys. Rep., 244, 77–202.CrossRefGoogle Scholar
[164] 1960. Conformal transformations of Kahler manifolds. Bull. Amer. Math. Soc., 66, 54–58.CrossRefGoogle Scholar
[165] 2006. Automorphic Forms and L-functions for the Group GL(n, ℝ). (Cambridge Studies in Advanced Mathematics, vol. 99). Cambridge University Press.Google Scholar
[166] , , and 2008. Bagger–Lambert Theory for general Lie algebras. JHEP, 0806, 075.CrossRefGoogle Scholar
[167] , , and 1994. Structure of Lie groups and Lie algebras. In: Lie Groups and Lie Algebras III. (Encyclopaedia of Mathematical Sciencesm, vol. 41). Springer.CrossRefGoogle Scholar
[169] , , and 1985. Anomaly free chiral theories in six-dimensions. Nucl. Phys., B254, 327.CrossRefGoogle Scholar
[170] , , and 2012. Superstring Theory. (Cambridge Monographs on Mathematical Physics). Cambridge University Press (2 volumes).Google Scholar
[172] , and 1969. Locally homogeneous complex manifolds. Acta Math., 123, 145–166.CrossRefGoogle Scholar
[173] 1984. Topics in Transcendental Algebraic Geometry. (Annals of Mathematical Studies.) Princeton University Press.Google Scholar
[174] , , , and 1985. Heterotic string theory. 1. The free heterotic string. Nucl. Phys., B256, 253.CrossRefGoogle Scholar
[175] , , , and 1986. Heterotic string theory. 2. The interacting heterotic string. Nucl. Phys., B267, 75.CrossRefGoogle Scholar
[176] , , and 2003. Calabi–Yau Manifolds and Related Geometries. (Universitext). Springer.CrossRefGoogle Scholar
[179] , , and 1983. Exceptional supergravity theories and the MAGIC square. Phys. Lett., B133, 72.CrossRefGoogle Scholar
[180] , , and 1986. Compact and noncompact gauged supergravity theories in five dimensions. Nucl. Phys., B272, 598.CrossRefGoogle Scholar
[182] , , and 1975. All possible generators of supersymmetries of the S-matrix. Nucl. Phys., B88, 257.CrossRefGoogle Scholar
[183] 1983. The boundary conditions for gauged supergravity. Phys. Lett., B126, 175–177.Google Scholar
[184] 2001. Differential Geometry, Lie Groups, and Symmetric Spaces. (Graduate Studies in Mathematics, vol. 34). American Mathematical Society.Google Scholar
[185] 1976. Differential Topology. (Graduate Texts in Mathematics, vol. 33). Springer.CrossRefGoogle Scholar
[186] 1995. New Topological Methods in Algebraic Geometry. (Classics in Mathematics). Springer.Google Scholar
[187] , and 2004. Analytic Number Theory. (Colloquium Publications, vol. 53). American Mathematical Society.Google Scholar
[188] , , , , , , , and 2003. Mirror Symmetry. (Clay Mathematics Monographs, vol. 1). American Mathematical Society.Google Scholar
[189] , , , , and 2008a. N = 4 superconformal Chern–Simons theories with hyper and twisted hyper multiplets. JHEP, 0807, 091.CrossRefGoogle Scholar
[190] , , , , and 2008b. N = 5,6 superconformal Chern–Simons theories and M2-branes on orbifolds. JHEP, 0809, 002.
[192] 1983. The positivity of gravitational energy and global supersymmetry. Commun. Math. Phys., 90, 545.CrossRefGoogle Scholar
[196] 1984d. The spontaneous breaking of supersymmetry in curved space-time. Nucl. Phys., B239, 541.CrossRefGoogle Scholar
[197] 1985. The minimal couplings and scalar potentials of the gauged N = 8 supergravities. Class. Quant. Grav., 2, 343.CrossRefGoogle Scholar
[198] 2003. New gauged N = 8, D = 4 supergravities. Class. Quant. Grav., 20, 5407–5424.CrossRefGoogle Scholar
[200] , and 1985. Supersymmetric sigma models and the heterotic string. Phys. Lett., 160 B, 398–402.Google Scholar
[201] 1994. Fibre Bundles. (Graduate Texts in Mathematics, vol. 20). American Mathematical Society.CrossRefGoogle Scholar
[202] 2004. Elliptic Curves. 2nd ed. (Graduate Texts in Mathematics, vol. 111). Springer.Google Scholar
[204] , and 2013. Aspects of 3d N = 2 Chern–Simons–matter theories. JHEP, 1307, 079.CrossRefGoogle Scholar
[205] , and 1981. Positivity of the Bondi gravitational mass. Phys. Lett., A85, 259–260.Google Scholar
[206] , and 1993. Localization for non-Abelian gauge actions. arXiv:alg-geom/9307001 [math.AG].
[207] 2005. Lectures on locally symmetric spaces and arithmetic groups. Pages 87–146 of: Lie Groups andAutomorphic Forms. American Mathematical Society.Google Scholar
[208] 2000. Compact Manifolds with Special Holonomy. (Oxford Mathematical Monographs). Oxford University Press.Google Scholar
[209] 2007. Riemannian Holonomy Groups and Calibrated Geometry. (Oxford Graduate Texts in Mathematics, vol. 12). Oxford University Press.Google Scholar
[210] 1981. Group disintegration. In: , and (eds.). Superspace and Supergravity. Cambridge University Press.Google Scholar
[212] , and 1992. Self—dual Chern—Simons systems with N = 3 extended supersymmetry. Phys. Rev., D46, 4691–4697.Google Scholar
[213] 2006. Enumerative Geometry and String Theory. (Student Mathematical Library, vol. 32). American Mathematical Society.
[214] 1995. Transformation Groups in Differential Geometry. (Classics in Mathematics). Springer.Google Scholar
[216] 1954. On Käahler varieties of the restricted type (an intrinsic characterization of algebraic varieties). Ann. Math., 60, 28–48.CrossRefGoogle Scholar
[217] 1986. Complex Manifolds and Deformation of Complex Structures. (Comprehensive Studies in Mathematics, vol. 283). Springer.CrossRefGoogle Scholar
[218] , and 1958. On deformations of complex analytic structures, I–II. Ann. Math., 67, 328–466.Google Scholar
[219] 1955. Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold. Trans. Amer. Math. Soc., 80, 528–542.CrossRefGoogle Scholar
[220] , and 1983. Supersymmetry and the division algebras. Nucl. Phys., B221, 357–380.Google Scholar
[221] , , and 2010. Global aspects of the space of 6D N = 1 supergravities. JHEP, 1011, 118.CrossRefGoogle Scholar
[222] , and 1991. Potentials for topological sigma models. Phys. Lett., B271, 101–108.Google Scholar
[224] 1995. Differential and Riemannian Manifolds. (Graduate Texts in Mathematics, vol. 160). Springer.CrossRefGoogle Scholar
[225] 1999. Fundamentals of Differential Geometry. Graduate Texts in Mathematics, vol. 191). Springer.CrossRefGoogle Scholar
[226] 1966. Volume of the fundamental domain for some arithmetical subgroup of Chevalley groups. Pages 235–257. of: Algebraic Groups and Discontinuous Subgroups. Proc. Symp. Pure Math. Vol. IX. American Mathematical Society.Google Scholar
[227] 2007a. Towards a classification of Lorentzian holonomy groups. J. Differential Geom., 76, 423–484.CrossRefGoogle Scholar
[228] 2007b. Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras. J. Differential Geom., 76, 423–484.Google Scholar
[231] 2005. Chern–Simons Theory, Matrix Models, and Topological Strings. (International Series of Monographs on Physics, vol. 131). Oxford University Press.CrossRefGoogle Scholar
[232] 1974. On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I: Derivation of necessary conditions. Ann. Inst. H. Poincari, A20, 153–188.Google Scholar
[233] , and Schwachhöfer. 1999. Classification of irreducible holonomies of torsion–free affine connections. Ann. Math., 150, 77–150.CrossRefGoogle Scholar
[234] , and 1939. The group of isometries of a Riemannian manifold. Ann. Math., 40, 400–416.Google Scholar
[235] , and 1974. Characteristic Classes. (Annals of Mathematical Studies, vol. 76). Princeton University Press.Google Scholar
[236] 2001. Black hole entropy, special geometry and strings. Fortsch. Phys., 49, 3–161.3.0.CO;2-#>CrossRefGoogle Scholar
[238] 2011. A Minicourse on Generalized Abelian Gauge Theory, Self–Dual Theories, and Differential Cohomology. Available at the author's webpage: http://www.physics.rutgers.edu/gmoore/SCGP-Minicourse.pdf. Accessed August 13, 2014.
[239] , and 2007. Ricci Flow and the Poincare Conjecture. (Clay Mathematics Monographs, vol. 3). American Mathematical Society.Google Scholar
[241] 2001. Introduction to Arithmetic Groups. Available as arXiv:math/0106063.
[242] 1934. The Calculus of Variations in the Large. (Colloquium Publications, vol. 18). American Mathematical Society (10th printing 2001).Google Scholar
[243] 1986. New heterotic string theories in uncompactified dimension < 10. Phys. Lett., B169, 41.CrossRefGoogle Scholar
[244] , , and 1987. A note on toroidal compactification of heterotic string theory. Nucl. Phys., B279, 369.CrossRefGoogle Scholar
[245] 1981a. A new gravitational energy expression with a simple positivity proof. Phys. Lett., A83, 241–242.Google Scholar
[247] 1981c. A new gravitational energy expression with a simple positivity proof. Phys. Lett., A83, 241–242.Google Scholar
[248] , and 2001a. Compact and noncompact gauged maximal supergravities in three-dimensions. JHEP, 0104, 022.CrossRefGoogle Scholar
[249] , and 2001b. Maximal gauged supergravity in three dimensions. Phys. Rev. Lett., 86, 1686–1689.CrossRefGoogle ScholarPubMed
[250] , and 2003. Chern–Simons versus Yang–Mills gaugings in three dimensions. Nucl. Phys., B668, 167–178.Google Scholar
[252] , and 1984. Matter and gauge couplings of N = 2 supergravity in six dimensions. Phys. Lett., B144, 187–192.Google Scholar
[253] , , , and 1984. Theory of Solitons: The Inverse Scattering Method. (Contemporary Soviet Mathematics). Plenum.Google Scholar
[254] 2005. A geometric proof of the Berger holonomy theorem. Ann. Math., 161, 579–588.CrossRefGoogle Scholar
[255] , and 2007. On the geometry of the string landscape and the swampland. Nucl. Phys., B766, 21–33.Google Scholar
[256] , , and 1984. Gauged maximally extended supergravity in seven dimensions. Phys. Lett., B143, 103.CrossRefGoogle Scholar
[258] 1998. String Theory. (Cambridge Monographs on Mathematical Physics). Cambridge University Press (2 volumes).Google Scholar
[259] , and 1989. Invariant metrics. In: Several Complex Variables, III. (Encyclopaedia of Mathematical Sciences, vol. 9). Springer.Google Scholar
[263] 2001. Geometry VI. Riemannian Geometry. (Encyclopaedia of Mathematical Sciences, vol. 91). Springer.Google Scholar
[264] 1960. Automorphic Functions and the Geometry of Classical Domains. Gordon and Breach.Google Scholar
[265] 1986. Self–duality for interacting fields: covariant field equations for six-dimensional chiral supergravities. Nucl. Phys., B276, 71–92.Google Scholar
[266] , and 1989. Supergravity in Diverse Dimensions, vols. 1 & 2. World Scientific.CrossRefGoogle Scholar
[267] 1989. Riemannian Geometry and Holonomy Groups. Longman Scientific and Technical.Google Scholar
[268] , and 1979a. Positivity of the total mass of a general space-time. Phys.Rev. Lett., 43, 1457–1459.CrossRefGoogle Scholar
[269] , and 1981. Proof of the positive mass theorem. 2. Commun. Math. Phys., 79, 231–260.CrossRefGoogle Scholar
[270] , and 1979b. On the proof of the positive mass conjecture in General Relativity. Commun. Math. Phys., 65, 45–76.CrossRefGoogle Scholar
[271] , and 1979c. Proof of the positive action conjecture in quantum gravity. Phys. Rev. Lett., 42, 547–548.CrossRefGoogle Scholar
[272] , and 2011. Charge lattices and consistency of 6D supergravity. JHEP, 1106, 001.CrossRefGoogle Scholar
[273] , and 1994a. Electric–magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang–Mills theory. Nucl. Phys., B426, 19–52.Google Scholar
[274] , and 1994b. Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD. Nucl. Phys., B431, 484–550.Google Scholar
[275] , and 1996. Comments on string dynamics in six-dimensions. Nucl. Phys., B471, 121–134.Google Scholar
[276] 1973. A Course in Arithmetic. (Graduate Texts in Mathematics, vol. 7). Springer.CrossRefGoogle Scholar
[277] , and 1995. Superconformal sigma models in higher than two dimensions. Nucl. Phys., B443, 70–84.Google Scholar
[282] 1991. Hyperkähler and quaternionic Kähler geometry. Math. Ann., 289, 421–450.CrossRefGoogle Scholar
[284] 1988. Harmonic Analysis on Symmetric Spaces and Applications. II. Springer.CrossRefGoogle Scholar
[285] 1987. Smoothness of the universal deformation space of compact Calabi–Yau manifolds and its Petersson–Weil metric. Pages 629–645. of: (ed.), Mathematical Aspects of String Theory. World Scientific.Google Scholar
[286] 1984. A new anomaly free chiral supergravity from compactification on K3. Phys. Lett., B139, 283–287.Google Scholar
[287] 2005. The String Landscape and the Swampland. e-print arXix:hep-th/0509212.
[288] , , and 1992. LiE, A Package for Lie Group Computations. Computer Algebra Nederland.Google Scholar
[290] 1999. Tools for Supersymmetry. (Lectures at the Spring School in Calimananesti, Romania). arXiv:hep-th/9910033.
[291] 1983. Superconformal tensor calculus in N = 1 and N = 2 super-gravity. In: Supersymmetry and Supergravity 1983. World Scientific.Google Scholar
[292] 1965. The theory of convex homogeneous cones. Pages 340–403. of: Transactions of the Moscow Mathematical Society for the Year 1963. American Mathematical Society.Google Scholar
[293] 2007a. Hodge Theory and Complex Algebraic Geometry I. (Cambridge Studies in Advanced Mathematics, vol. 76). Cambridge University Press.Google Scholar
[294] 2007b. Hodge Theory and Complex Algebraic Geometry II. (Cambridge Studies in Advanced Mathematics, vol. 77). Cambridge University Press.
[295] 1989. Parallel spinors and parallel forms. Ann. Global Anal. Geom., 7, 59–68.CrossRefGoogle Scholar
[296] 1972. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley.Google Scholar
[297] , and 1992. Supersymmetry and Supergravity (Revised edn.). (Princeton Series in Physics). Princeton University Press.Google Scholar
[298] 1990. Introduction to Supersymmetry and Supergravity. (Revised and extended second edn.). World Scientific.CrossRefGoogle Scholar
[300] 1981. A new proof of the positive energy theorem. Commun. Math. Phys., 80, 381–402.CrossRefGoogle Scholar
[302] 1982b. Supersymmetry and Morse theory. J. Differential Geom., 17, 661–692.CrossRefGoogle Scholar
[303] 1983a. Current algebra, baryons, and quark confinement. Nucl. Phys., B223, 433–444.Google Scholar
[307] 1987. Elliptic genera and quantum field theory. Commun. Math. Phys., 109, 525–536.CrossRefGoogle Scholar
[308] 1988a. 2+1 dimensional supergravity as an exactly soluble system. Nucl. Phys., B 311, 46–78.Google Scholar
[309] 1988b. Topological quantum field theory. Commun. Math. Phys., 117, 411–449.CrossRefGoogle Scholar
[311] 1989. Quantum field theory and the Jones polynomial. Commun. Math. Phys., 121, 351.CrossRefGoogle Scholar
[312] 1992. Two–dimensional gauge theories revisited. J. Geom. Phys., 9, 303–368.CrossRefGoogle Scholar
[314] 1995b. Some Comments on String Dynamics. e-preprint arXiv:hep-th/9507121.
[315] 1996. talk given at the Newton Institute for Mathematical Sciences, Cambridge.
[317] 2005. Non—Abelian localization for Chern—Simons theory. J. Geom. Phys., 70, 183–323.Google Scholar
[318] , and 1982. Quantization of Newton's constant in certain super-gravity theories. Phys. Lett., B 115, 202.CrossRefGoogle Scholar
[319] 1962. Discrete groups, symmetric spaces, and global holonomy. Amer. J. Math., 84, 527–542.CrossRefGoogle Scholar
[320] 1965. Complex homogeneous contact manifolds and quaternionic symmetric spaces. J. Math. Mech., 14, 1033–1047.Google Scholar
[322] 1967. Holonomy groups of indefinite metrics. Pac. J. Math., 20, 351–392.CrossRefGoogle Scholar
[323] 2000. Theory of Complex Homogenous Bounded Domains. Science Press/Kluwer Academic Publishers.Google Scholar
[325] 2011. The Theory of Lie Derivatives and its Applications. Nabu Press.
[326] 1978. On the Ricci curvature of a compact Kahler manifold and the complex Monge—Ampere equation. I. Commun. Pure Appl. Math., 31, 339–411.CrossRefGoogle Scholar
[327] 1986. Irreversibility of the flux of the renormalization group in a 2D field theory. JETP Lett., 43, 730–732.Google Scholar