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

Nuclear Physics B (Impact Factor: 3.93). 11/2011; 866(1). DOI: 10.1016/j.nuclphysb.2012.08.015
Source: arXiv


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, Oct 09, 2015
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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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    ABSTRACT: We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d N=2 "Lens space theory" $T[L(p,1)]$ and the partition function of complex Chern-Simons theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$ partition function of Chern-Simons theory arises from the index of a free theory. For large $p$, we find that the index of $T[L(p,1)]$ becomes a constant independent of $p$. In addition, we study $T[L(p,1)]$ on the squashed three-sphere $S^3_b$. This enables us to see clearly, at the level of partition function, to what extent $G_\mathbb{C}$ complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group $G$.
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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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    ABSTRACT: We compute the supersymmetric Rényi entropies across a spherical entanglement surface in \( \mathcal{N}=4 \) SU(N) SYM theory using localization on the four-dimensional ellipsoid. We extract the leading result at large N and λ and match its universal part to a gravity calculation involving a hyperbolically sliced supersymmetric black hole solution of \( \mathcal{N}={4}^{+} \) SU(2) × U(1) gauged supergravity in five dimensions. We repeat the analysis in the presence of a Wilson loop insertion and find again a perfect match with the dual string theory. Understanding the Wilson loop operator requires knowledge of the full ten-dimensional IIB supergravity solution which we elaborate upon.
    Journal of High Energy Physics 12/2014; 2014(12). DOI:10.1007/JHEP12(2014)001 · 6.11 Impact Factor
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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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