Abstract
We find new supersymmetric backgrounds of ${\cal N} = 8$ gauged supergravity in four Euclidean dimensions that are dual to deformations of ABJM theory on $S^3$. The deformations encode the most general choice of $U(1)_R$ symmetry used to define the theory on $S^3$. We work within an ${\cal N} = 2$ truncation of the ${\cal N} = 8$ supergravity theory obtained via a group theory argument. We find perfect agreement between the $S^3$ free energy computed from our supergravity backgrounds and the previous field theory computations of the same quantity based on supersymmetric localization and matrix model techniques.
Highlights
The past few years have seen much progress in our understanding of supersymmetric quantum field theories in 2+1 space-time dimensions
We find perfect agreement between the S3 free energy computed from our supergravity backgrounds and the previous field theory computations of the same quantity based on supersymmetric localization and matrix model techniques
From the perspective of string theory and the AdS/CFT duality [1,2,3], a significant result was the discovery of (2 + 1)-dimensional superconformal field theories (SCFTs) on N coincident M2-branes placed at the tip of various Calabi-Yau cones
Summary
The past few years have seen much progress in our understanding of supersymmetric quantum field theories in 2+1 space-time dimensions. The fourth subtlety is related to the last point just mentioned It is not the renormalized bulk on-shell action that should be identified with the boundary free energy F , but instead its Legendre transform with respect to the leading asymptotic behavior of zα + zα. Such a Legendre transform was introduced in [28], where it was explained that the Legendre transform is necessary for obtaining the correct correlation functions in the field theory whose gravity dual contains a scalar with alternate boundary conditions. Many of the details of our computations are relegated to the appendices
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