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2 results

  • 13 - Toroidal compactication

  • from Part II - Extensions and applications
  • Eric D'Hoker, University of California, Los Angeles, Justin Kaidi, Kyushu University
  • Book:
    Modular Forms and String Theory
    Published online:
    28 November 2024
    Print publication:
    12 December 2024, pp 259-273

  • 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.