Background constraints in the infinite tension limit of the heterotic string

TL;DR

This paper explores how classical background constraints in heterotic string theory emerge from BRST charge nilpotency in the pure spinor formalism, especially in the infinite tension limit, revealing a unified approach.

Contribution

It demonstrates that all ten-dimensional background constraints can be derived from a single nilpotency condition within the pure spinor framework, highlighting a novel unification.

Findings

Constraints are derived from BRST nilpotency.

Sectorization simplifies the constraint analysis.

Unified derivation of supergravity and super Yang-Mills constraints.

Abstract

In this work we investigate the classical constraints imposed on the supergravity and super Yang-Mills backgrounds in the $\alpha'\to 0$ limit of the heterotic string using the pure spinor formalism. Guided by the recently observed sectorization of the model, we show that all the ten-dimensional constraints are elegantly obtained from the single condition of nilpotency of the BRST charge.