CFTs on Riemann Surfaces of genus $g\geq 1$

TL;DR

This paper derives explicit formulas for 2-point and higher N-point functions of the Virasoro field on hyperelliptic Riemann surfaces of genus g≥1, using algebraic geometry methods, with applications to minimal models.

Contribution

It provides new explicit formulas for Virasoro N-point functions on hyperelliptic Riemann surfaces, including a graph representation and applications to minimal models.

Findings

Explicit formulas for 2-point functions on hyperelliptic surfaces.

Inductive construction of N-point functions with graph representations.

Application to the (2,5) minimal model.

Abstract

$N$-point functions of holomorphic fields in conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulas for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus $g\geq 1$. Virasoro $N$-point functions for higher $N$ are obtained inductively, and we show that they have a nice graph representation. We discuss the 3-point function with application to the $(2,5)$ minimal model.