Anomaly, Fluxes and (2,0) Heterotic-String Compactifications

TL;DR

This paper calculates two-loop corrections to heterotic-string backgrounds with (2,0) supersymmetry, revealing deformations of Calabi-Yau geometries to Hermitian structures and analyzing anomaly cancellation and moduli stability.

Contribution

It provides the first detailed analysis of $ ext{α'}$ corrections to (2,0) heterotic-string compactifications, including explicit computations for conifold and Calabi-Yau metrics.

Findings

Calabi-Yau geometry deforms to Hermitian structure at first order in α'

Heterotic anomaly cancellation does not lift moduli at first order

Explicit corrections computed for conifold and U(n)-invariant Calabi-Yau metrics

Abstract

We compute the corrections to heterotic-string backgrounds with (2,0) world-sheet supersymmetry, up to two loops in sigma-model perturbation theory. We investigate the conditions for these backgrounds to preserve spacetime supersymmetry and we find that a sufficient requirement for consistency is the applicability of the $\partial\bar\partial$-lemma. In particular, we investigate the $\alpha'$ corrections to (2,0) heterotic-string compactifications and we find that the Calabi-Yau geometry of the internal space is deformed to a Hermitian one. We show that at first order in $\alpha'$, the heterotic anomaly-cancellation mechanism does not induce any lifting of moduli. We explicitly compute the corrections to the conifold and to the U(n)-invariant Calabi-Yau metric at first order in $\alpha'$. We also find a generalization of the gauge-field equations, compatible with the Donaldson equations on conformally-balanced Hermitian manifolds.