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13 - Toroidal compactication

from Part II - Extensions and applications

Published online by Cambridge University Press:  aN Invalid Date NaN

Eric D'Hoker  and
Justin Kaidi
Eric D'Hoker
Affiliation:
University of California, Los Angeles
Justin Kaidi
Affiliation:
Kyushu University
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Summary

In this chapter, we discuss the modular properties of quantum field theories of scalar fields that take values in a d-dimensional torus with a flat metric and a constant anti-symmetric tensor. The problem is of great interest in quantum field theory and string theory in view of the fact that such toroidal compactifications admit solutions using free-field theory methods on the worldsheet, preserve Poincaré supersymmetries and may be used to relate different perturbative string theories via T-duality. Toroidal compactifications produce large duality groups, which we shall derive and which generalize the full modular group SL(2,Z). The quantum field theories of toroidal compactification on a worldsheet torus for a singular modulus is shown to be a rational conformal field theory.

Keywords

toroidal compactificationlatticesT-dualityrational conformal field theorycomplex multiplication
Type
Chapter
Information
Modular Forms and String Theory , pp. 259 - 273
Publisher: Cambridge University Press
Print publication year: 2024

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