Heterotic String Sigma Models: Discrete Light Cone Quantization and Its Current-Current Deformation

TL;DR

This paper introduces a novel heterotic string sigma model derived from a BPS decoupling limit, providing a new framework for understanding heterotic strings in non-Lorentzian geometries and their deformations.

Contribution

It constructs a self-contained heterotic string sigma model from a BPS limit, extending non-relativistic string formulations to heterotic cases and defining heterotic string theory via discrete light cone quantization.

Findings

The worldsheet theory offers a first-principles definition of heterotic strings in DLCQ.

A current-current deformation recovers conventional heterotic string theory.

The model is consistent with non-Lorentzian supergravity and anomaly cancellation.

Abstract

We propose a two-dimensional superstring sigma model that defines a self-contained corner of heterotic string theory, whose second quantization is heterotic matrix string theory. This worldsheet theory arises from a BPS decoupling limit that zooms in on the heterotic string, under which the target space geometry becomes non-Lorentzian. This construction generalizes the Gomis-Ooguri formulation of non-relativistic string theory to the heterotic case. We show how such a worldsheet theory provides a first-principles definition of the heterotic string in the discrete light cone quantization via T-duality. By turning on a current-current deformation akin to a $T\bar{T}$ deformation, the conventional heterotic string theory with a Lorentzian target space is recovered. We analyze the gauge and gravitational anomalies with respect to the lowest-order quantum corrections in the sigma model and show how the worldsheet theory is consistent with non-Lorentzian supergravity in the target space.