On a gravity dual to flavored topological quantum mechanics
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Springer
Received: June 17, 2020 Accepted: September 20, 2020 Published: October 19, 2020
Andrey Feldman Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel
E-mail: [email protected] Abstract: In this paper, we propose a generalization of the AdS2 /CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in N = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4 × S7 /Zk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence ArXiv ePrint: 2005.12228
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)113
JHEP10(2020)113
On a gravity dual to flavored topological quantum mechanics
Contents 1 Introduction
1
2 AdS2 side
2 3 3 4 4 5 8 11
4 Bulk symmetry and dynamics 4.1 Single-trace operators 4.2 Jacobi identities 4.3 The double-trace contribution
12 13 14 15
5 Conclusions and future directions
18
1
Introduction
A holographic duality we consider in this paper is a generalization of the duality between the 1d topological matrix quantum mechanics (QM), which can be viewed as a subsector of the 3d N = 4 gauge theory [2–4], and a non-linear higher-derivative generalization of the Yang-Mills theory in the AdS2 background. The first example of such a duality was given in [1], where an equivalence of the 1d topological QM of interacting U(N ) gauge field, a e and two adjoint X, X e scalars, and a non-linear Yangfundamental Q, anti-fundamental Q, 2 Mills theory on AdS2 with the gauge group SDiff S of area-preserving diffeomorphisms of the 2-sphere, was considered. The QM theory we work with is the generalization of the theory studied in [1] to the case of k fundamental scalars, and non-vanishing Fayet-Iliopoulos (FI) term. This theory is particularly interesting, because it arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, with the gauge coupling ∆ and the FI parameter identified with two equivariant parameters of the Ω-deformation [5–8].1 1
This brane configuration is equivalent to a stack of M2-branes in the Taub-NUT background in the Ω-deformed M-theory.
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