Two loop mass renormalisation in heterotic string theory: NS states

TL;DR

This paper calculates the two-loop mass renormalization for NS states in heterotic string theory, using vertical integration and boundary term techniques to handle spurious poles and moduli space boundaries.

Contribution

It introduces a method to compute two-loop mass renormalization in heterotic string theory by implementing vertical integration and boundary term techniques.

Findings

Successfully expressed the amplitude as a boundary term.

Identified the 1PI region of the moduli space.

Determined the relevant integrands and integration regions.

Abstract

In this work computation of the renormalised mass at two loop order for the NS sector of heterotic string theory is attempted. We first implement the vertical integration prescription for choosing a section avoiding the spurious poles due to the presence of a required number of picture changing operators. As a result the relevant amplitude on genus 2 Riemann surface can be written as a boundary term. We then identify the 1PI region of the moduli space having chosen a gluing compatible local coordinates around the external punctures. We also identify the relevant integrands and the relevant region of integration for the modular parameters at the boundary.