Article

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

(Impact Factor: 3.93). 11/2011; 866(1). DOI: 10.1016/j.nuclphysb.2012.08.015
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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Available from: James Sparks
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• "There are two kinds of squashed three-spheres breaking the SO(4) isometry of the round S 3 : the first one preserves SU (2) × U (1) isometry while the second one preserves U (1) × U (1) [33]. However, despite the geometry being different, the partition functions of 3d N = 2 theories that one gets are the same [33] [34] [35] [36]. In fact, as was shown in [37], three-sphere partition functions of N = 2 theories only admit a one-parameter deformation. "
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• "Thus one ends up in a situation where the holographic dual of a theory on the ellipsoid is given by a bulk solution with hyperbolic spatial slices, namely a hyperbolic black hole. For direct gravity duals of three-dimensional gauge theories on other kinds of ellipsoids see [15] [16]. "
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• "Refs. [17] [18] [19] constructed four-dimensional "
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ABSTRACT: We find the gravity dual of N = 2[superscript *] super-Yang-Mills theory on S [superscript 4] and use holography to calculate the universal contribution to the corresponding S [superscript 4] free energy at large N and large ’t Hooft coupling. Our result matches the expression previously computed using supersymmetric localization in the field theory. This match represents a non-trivial precision test of holography in a non-conformal, Euclidean signature setting.
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