Modular differential equations for torus one-point functions

Abstract

It is shown that in a rational conformal field theory every torus one-point function of a given highest weight state satisfies a modular differential equation. We derive and solve these differential equations explicitly for some Virasoro minimal models. In general, however, the resulting amplitudes do not seem to be expressible in terms of standard transcendental functions.

19 pages, LaTeX; reference added

References in corpus (5)

• Logarithmic torus amplitudes
• Constraints on extremal self-dual CFTs
• Prospects for Yukawa Unified SO(10) SUSY GUTs at the CERN LHC
• Vector-valued modular functions for the modular group and the hypergeometric equation
• Differential equations and conformal field theories

Cited by in corpus (1)

• Contour Integral Representations for the Characters of Logarithmic CFTs