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from Part II - Extensions and applications
Published online by Cambridge University Press: 28 November 2024
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.
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