Supersymmetric solutions to Euclidean Romans supergravity

TL;DR

This paper characterizes supersymmetric solutions in Euclidean Romans supergravity, linking them to differential constraints on SU(2) structures, and applies these to holography, Wilson loops, and new solutions.

Contribution

It establishes a one-to-one correspondence between supersymmetric solutions and SU(2) structures, and derives holographic duals for Wilson loops and squashed geometries.

Findings

Supersymmetric solutions correspond to differential constraints on SU(2) structures.

Derived holographic duals for BPS Wilson loops matching field theory.

Constructed new analytic solutions and holographic duals to squashed Sasaki-Einstein backgrounds.

Abstract

We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied by the authors, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions.