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

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 ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$, 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 ${\alpha }^{\prime }$. We also find a generalization of the gauge-field equations, compatible with the Donaldson equations on conformally-balanced Hermitian manifolds.

24 pages. v2: Reference added

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