Lattice perturbation theory for the null cusp string

TL;DR

This paper develops a lattice discretization of the gauge-fixed Green-Schwarz superstring on a null cusp background that preserves key symmetries and analyzes its renormalization properties at one loop.

Contribution

It introduces a symmetry-preserving lattice setup for the superstring and studies its one-loop renormalizability, identifying necessary parameter adjustments to handle divergences.

Findings

Preserves global U(1)×SU(4) symmetry on the lattice

Identifies UV divergences requiring two parameters for renormalization

Demonstrates one-loop renormalizability with parameter tuning

Abstract

We reconsider the problem of discretising the worldsheet for the gauge-fixed Green-Schwarz superstring on a null cusp background, and present a setup which fully preserves its global $U(1)\times SU(4)$ symmetry. We discuss divergences by power counting on the lattice, and study renormalizability at one loop with the example of one-point functions and one bosonic correlator of the worldsheet excitations. In order to remove UV divergences at one loop, it is necessary to introduce two extra parameters in the action, which need to be either fine-tuned at tree level or renormalized at one-loop.