A 2d/1d Holographic Duality

Márk Mezei; Silviu S. Pufu; Yifan Wang

paper

A 2d/1d Holographic Duality

arXiv:1703.08749

Abstract

We propose $A d S_{2}$ /CFT $_{1}$ dualities between exactly solvable topological quantum mechanics theories with vector or matrix large $N$ limits (on the boundary) and weakly coupled gauge theories on a fixed $A d S_{2}$ background (in the bulk). The boundary theories can be embedded as 1d sectors of 3d $N = 4$ superconformal field theories with holographic duals, from which they can be obtained using supersymmetric localization. We study a few examples of such 1d theories: theories with vector large $N$ limits that are embedded into 3d theories of many free massless hypermultiplets with $A d S_{4}$ higher spin duals; and a 1d theory with a matrix large $N$ limit embedded into the 3d ABJM theory at Chern-Simons level $k = 1$ , which has an $A d S_{4}$ supergravity dual. We propose that the $U (N)$ singlet sectors of the 1d vector models are dual to 2d gauge theories on $A d S_{2}$ whose gauge algebras are finite dimensional and whose full non-linear actions we completely determine in some cases. The 1d theory embedded into ABJM theory has a $Z_{2}$ -invariant sector dual to a 2d gauge theory on $A d S_{2}$ whose gauge algebra is the infinite dimensional algebra of area preserving diffeomorphisms of a two-sphere. We provide evidence that the 2d gauge theories on $A d S_{2}$ can be obtained from localizing the $A d S_{4}$ duals of the 3d SCFTs mentioned above, and thus argue that our 2d/1d dualities can be obtained via supersymmetric localization on both sides of their parent $A d S_{4}$ /CFT $_{3}$ dualities. We discuss the boundary terms required by holographic renormalization in the 2d gauge theories on $A d S_{2}$ and show how they arise from supersymmetric localization.

70 pages plus appendices, 4 figures

A 2d/1d Holographic Duality

Abstract

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