On the holomorphic factorization for superconformal fields

TL;DR

This paper proves the holomorphic factorization of partition functions for free superconformal fields on compact Riemann surfaces, demonstrating how these functions decompose into holomorphic and anti-holomorphic parts in a superconformal setting.

Contribution

It establishes the holomorphic factorization property for superconformal field partition functions for generic central charge values, extending known results to the superconformal case.

Findings

Partition functions factorize holomorphically on Riemann surfaces.

The factorization holds for generic central charge values.

Partition functions depend on superconformal moduli via Beltrami coefficients.

Abstract

For a generic value of the central charge, we prove the holomorphic factorization of partition functions for free superconformal fields which are defined on a compact Riemann surface without boundary. The partition functions are viewed as functionals of the Beltrami coefficients and their fermionic partners which variables parametrize superconformal classes of metrics.