Holography for $\mathcal{N}=1^{\ast }$ on $S^4$ and Supergravity

Abstract

We study the $SO(3)$ sector of the $\mathcal{N}=1^{\ast }$ mass deformation of $\mathcal{N}=4$ super Yang-Mills on $S^4$. The gravity dual of this sector is $\mathcal{N}=2$ supergravity coupled to two hypermultiplets. The scalar fields in the hypermultiplets span a quaternionic-Kahler manifold that is described by the coset $G_{2,2}/SU(2)\times SU(2)$. We use the $\mathcal{N}=2$ supergravity dual to study field configurations in the bulk that feature analytical solutions, and compute the corresponding $S^4$ free energy using the procedure of holographic renormalization. We find that the free energy of these configurations is quadratic in the mass and show that it is devoid of unphysical ambiguities, hence providing an analytical prediction for the $\mathcal{N}=1$ four-sphere partition function at large 't Hooft coupling in the planar limit.

arXiv comment45 pages

References in corpus (14)

• General matter coupled N=2, D=5 gauged supergravity
• Comments on twisted indices in 3d supersymmetric gauge theories
• Sphere Partition Functions and the Zamolodchikov Metric
• Localization on Hopf surfaces
• Broken sigma-model isometries in very special geometry
• N=1 Supersymmetric Renormalization Group Flows from IIB Supergravity
• Rigorous Test of Non-conformal Holography: Wilson Loops in N=2* Theory
• Evidence for Large-N Phase Transitions in N=2* Theory
• Anatomy of Two Holographic Renormalization Group Flows
• Supersymmetric partition functions on Riemann surfaces
• Curved BPS domain wall solutions in five-dimensional gauged supergravity
• Bent BPS domain walls of D=5 N=2 gauged supergravity coupled to hypermultiplets
• Instantons and Wormholes in N=2 supergravity
• Instantons and Wormholes for the Universal Hypermultiplet

Cited by in corpus (1)

• Analytic continuation of dimensions in supersymmetric localization