The gravity dual of supersymmetric gauge theories on a squashed three-sphere
Abstract
We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a U(1) x U(1)-invariant squashed three-sphere, with a non-trivial background gauge field. This is described by a supersymmetric solution of four-dimensional N=2 gauged supergravity with a non-trivial instanton for the graviphoton field. The particular gauge theory in turn determines the lift to a solution of eleven-dimensional supergravity. We compute the partition function for a class of Chern-Simons quiver gauge theories on both sides of the duality, in the large N limit, finding precise agreement for the functional dependence on the squashing parameter. This constitutes an exact check of the gauge/gravity correspondence in a non-conformally invariant setting.
Keywords
Cite
@article{arxiv.1110.6400,
title = {The gravity dual of supersymmetric gauge theories on a squashed three-sphere},
author = {Dario Martelli and Achilleas Passias and James Sparks},
journal= {arXiv preprint arXiv:1110.6400},
year = {2015}
}
Comments
37 pages. v2: typos fixed, references added, new section 2.5 added discussing the solution in standard global coordinates; v3: more typos fixed, version published on Nucl. Phys. B