NSR measures on hyperelliptic locus and non-renormalization of 1,2,3-point functions

TL;DR

This paper shows that certain sums over spin-structures involving fermionic correlators and NSR measures vanish on hyperelliptic loci, supporting their validity and contributing to non-renormalization theorems in superstring theory.

Contribution

It provides evidence that NSR measures satisfy vanishing sums on hyperelliptic loci, advancing the understanding of non-renormalization in superstring amplitudes.

Findings

Sums over spin-structures vanish on hyperelliptic loci

Supports validity of NSR measures

Progress towards non-renormalization proofs

Abstract

We demonstrate (under a modest assumption) that the sums over spin-structures of the simplest combinations of fermionic correlators (Szego kernels) and DHP/CDG/Grushevsky NSR measures vanish at least on the hyperelliptic loci in the moduli space of Riemann surfaces -- despite the violation of the theta_e^4 hypothesis at g>2. This provides an additional important support to validity of these measures and is also a step towards a proof of the non-renormalization theorems in the NSR approach.