Modular differential equations for torus one-point functions

TL;DR

This paper demonstrates that torus one-point functions in rational conformal field theories satisfy modular differential equations, deriving explicit solutions for some models and discussing the complexity of their expressions.

Contribution

It introduces a general framework linking torus one-point functions to modular differential equations and provides explicit solutions for specific Virasoro minimal models.

Findings

Torus one-point functions satisfy modular differential equations.

Explicit solutions are derived for certain Virasoro minimal models.

General amplitudes may not be expressible with standard transcendental 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.