Article

# The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere

11/2011;
Source: arXiv

ABSTRACT We present the gravity dual to a class of three-dimensional N=2
supersymmetric gauge theories on a biaxially squashed three-sphere, with a
non-trivial background gauge field. This is described by a 1/2 BPS Euclidean
solution of four-dimensional N=2 gauged supergravity, consisting of a
Taub-NUT-AdS metric with a non-trivial instanton for the graviphoton field. The
holographic free energy of this solution agrees precisely with the large N
limit of the free energy obtained from the localized partition function of a
class of Chern-Simons quiver gauge theories. We also discuss a different
supersymmetric solution, whose boundary is a biaxially squashed Lens space
S^3/Z_2 with a topologically non-trivial background gauge field. This metric is
of Eguchi-Hanson-AdS type, although it is not Einstein, and has a single unit
of gauge field flux through the S^2 cycle.

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### Keywords

biaxially squashed Lens space

biaxially squashed three-sphere

Eguchi-Hanson-AdS type

graviphoton field

gravity dual

holographic free energy

localized partition function

non-trivial background gauge field

non-trivial instanton

S^2 cycle

single unit

topologically non-trivial background gauge field