Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions

Abstract

We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the supersymmetric backgrounds of ten-dimensional conformal supergravity and those of eleven-dimensional Poincaré supergravity.

On the algebraic structure of Killing superalgebras

“…Identities (26), (28) and (29) show that Φ is a Lie superalgebra anti-homomorphism. The fact that Φ is an (anti)embedding of realizable filtered subdeformations of p is immediate, as well as the last two claims of the theorem.…”

“…In more recent times, it made its appearance in the context of the AdS/CFT correspondence [17,18], brane solutions [19,20,21], plane waves [22,23] and homogeneous backgrounds [24], with the general construction appearing for the first time in [25] for d=11 and [26] for d=10 supergravities. Since then, a number of other supergravity theories have been treated, such as d=6 [27], d=10 conformal in [28] and d=4 (off-shell, minimal) in [29].…”