Book contents
- Frontmatter
- Contents
- Preface
- I Supersymmetry: the physical and mathematical foundations
- II Globally supersymmetric theories
- 10 Supersymmetric point particle mechanics
- 11 Pseudoclassical mechanics of superpoint particles
- 12 Supersymmetric field theories in two space–time dimensions
- 13 Spontaneous supersymmetry breaking
- 14 Vector and chiral superfields in four-dimensional space–time
- 15 The Wess–Zumino model
- 16 The supersymmetric Maxwell and Yang–Mills theories
- 17 Supersymmetric quantum field theories and their applications
- 18 Finite quantum field theories
- 19 The supercurrent and anomaly supermultiplets
- III Supergravities: locally supersymmetric theories
- IV Conclusion
- References
- Index
19 - The supercurrent and anomaly supermultiplets
Published online by Cambridge University Press: 01 June 2011
- Frontmatter
- Contents
- Preface
- I Supersymmetry: the physical and mathematical foundations
- II Globally supersymmetric theories
- 10 Supersymmetric point particle mechanics
- 11 Pseudoclassical mechanics of superpoint particles
- 12 Supersymmetric field theories in two space–time dimensions
- 13 Spontaneous supersymmetry breaking
- 14 Vector and chiral superfields in four-dimensional space–time
- 15 The Wess–Zumino model
- 16 The supersymmetric Maxwell and Yang–Mills theories
- 17 Supersymmetric quantum field theories and their applications
- 18 Finite quantum field theories
- 19 The supercurrent and anomaly supermultiplets
- III Supergravities: locally supersymmetric theories
- IV Conclusion
- References
- Index
Summary
When the fields that appear in the lagrangian of a classical theory undergo the transformations dictated by an ordinary Lie algebra, the change of the action itself, according to the celebrated theorem of Emmy Noether, can be cast into the form of a space–time integral of the divergence of some currents. In particular, when the action is invariant under the effect of the Lie algebra these Noether currents (their number equal to the Lie algebra's dimension) are conserved. Not surprisingly, this theorem admits a straightforward generalization to the case of Lie superalgebras, i.e., to the supersymmetric case. Along with the vectorial and tensorial Bose currents, there will exist spinorial Fermi currents in this case (see chapter 1). In both ordinary and supersymmetric quantum theories, anomalies can break the classical conservation laws.
We shall discuss here the classical conservation laws and their quantum demise via anomalies in a supersymmetric theory. As we shall see, the existence of a supermultiplet containing both the energy–momentum tensor and the chiral current at the classical level can lead to some paradoxical results in the quantum theory, unless sufficient care is exercised.
Consider a field theory which classically is both N = 1 Poincaré supersymmetric and conformally invariant, i.e., invariant under the full N = 1 superconformal algebra su(2,2|1) (see chapter 4).
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- Information
- Introduction to Supersymmetry , pp. 90 - 94Publisher: Cambridge University PressPrint publication year: 1986