Geometry and supersymmetry of heterotic warped flux AdS backgrounds

TL;DR

This paper classifies warped flux AdS backgrounds in heterotic supergravity, revealing the geometric structures and supersymmetry preservation conditions, and introduces a new Lichnerowicz theorem with alpha' corrections.

Contribution

It provides a comprehensive classification of heterotic warped flux AdS backgrounds up to two-loop order, detailing the geometric structures and supersymmetry properties of solutions.

Findings

No AdS_n backgrounds with n ≠ 3 under mild assumptions.

AdS_3 backgrounds have constant warp factor and are of the form AdS_3 × M^7.

M^7 admits specific G-structures depending on the number of supersymmetries.

Abstract

We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with $n\not=3$. Moreover the warp factor of AdS$_3$ backgrounds is constant, the geometry is a product $AdS_3\times M^7$ and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of $M^7$ has been specified in all cases. For 2 supersymmetries, it has been found that $M^7$ admits a suitably restricted $G_2$ structure. For 4 supersymmetries, $M^7$ has an $SU(3)$ structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, $M^7$ has an $SU(2)$ structure and can be described locally as a $S^3$ fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-K\"ahler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of $\alpha'$ corrections.