CFTs on Riemann Surfaces of genus $g\geq 1$: Dependence on moduli

TL;DR

This paper investigates how Virasoro $N$-point functions in conformal field theories depend on the moduli of Riemann surfaces, introducing an algebraic geometric approach applicable to hyperelliptic cases.

Contribution

It introduces an algebraic geometric method to analyze the moduli dependence of Virasoro $N$-point functions on hyperelliptic Riemann surfaces.

Findings

Dependence of Virasoro $N$-point functions on moduli characterized.

Applicable to all hyperelliptic Riemann surfaces.

Provides a new algebraic geometric framework.

Abstract

The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approach that applies to any hyperelliptic Riemann surface.