Background constraints in the infinite tension limit of the heterotic string

TL;DR

The paper investigates the α'→0 (infinite-tension) limit of the heterotic string in the pure spinor, sectorized ambitwistor framework. By demanding nilpotency of the BRST charge in curved backgrounds, it derives the ten-dimensional supergravity and super Yang-Mills constraints in superspace, first from the curved supergravity sector and then including YM couplings. The analysis shows how background fields appear as deformations of a free, chiral action and identifies the precise algebraic conditions—on torsion, H-flux, curvature, and YM field strengths—that ensure BRST consistency. These results connect the infinite-tension heterotic string to the ambitwistor/CHY program and lay groundwork for future quantum treatments and amplitude calculations within this sectorized framework.

Abstract

In this work we investigate the classical constraints imposed on the supergravity and super Yang-Mills backgrounds in the $α'\to 0$ 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.