Anomaly corrected heterotic horizons

Abstract

We consider supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory. We identify the conditions for the horizons to admit enhancement of supersymmetry. We show that solutions which undergo supersymmetry enhancement exhibit an sl(2, R) symmetry, and we describe the geometry of their horizon sections. We also prove a modified Lichnerowicz type theorem, incorporating α ′ corrections, which relates Killing spinors to zero modes of near-horizon Dirac operators. Furthermore, we demonstrate that there are no AdS 2 solutions in heterotic supergravity up to second order in α ′ for which the fields are smooth and the internal space is smooth and compact without boundary. We investigate a class of nearly supersymmetric horizons, for which the gravitino Killing spinor equation is satisfied on the spatial cross sections but not the dilatino one, and present a description of their geometry.

AdS5 backgrounds with 24 supersymmetries

“…This is because any AdS d+1 background can locally be written as a warped product ds 2 (AdS d+1 ) = dy 2 + A 2 (y)ds 2 (AdS d ) for some function A which has been determined in e.g. [31]. For d = 2, this has previously been established in [32].…”

“…On expanding this expression out, and adding it to (4.29), one obtains the condition 31) or equivalently…”

On supersymmetric anti-de Sitter, de Sitter and Minkowski flux backgrounds

“…This has been explored before in the literature [19]- [22]. Here we shall give a description which is suitable for our purposes and resembles the form used in [23]. It is known that AdS n+1 space can be described as a conic…”

Symmetry enhancement of extremal horizons in D = 5 supergravity

“…In general, higher derivative supergravity theories have extremely complicated field equations, which makes a systematic analysis of the near-horizon geometries challenging. One theory for which the field equations are relatively simple is heterotic supergravity with α ′ corrections, the near-horizon analysis in this theory has already been considered in [38]. In the context of D = 5 theories, higher derivative theories have been constructed in [39], and the nearhorizon analysis has been considered in [40], however the analysis in this case assumes that the black hole timelike isometry ∂ ∂u arises as a Killing spinor bilinear.…”