On a Gravity Dual to Flavored Topological Quantum Mechanics

Abstract: In this paper, we propose a generalization of the $\mathrm{AdS_2/CFT_1}$ correspondence constructed by Mezei, Pufu and Wang in \cite{MezeiPufuWang}, which is the duality between 2d Yang-Mills theory with higher derivatives in the $\mathrm{AdS}_2$ background, and 1d topological quantum mechanics of two adjoint and two fundamental $\mathrm{U}(N)$ 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 \cite{MezeiPufuWang}, which arises as the effective field theory living on the intersection of stacks of $N$ D2-branes and $k$ D6-branes in the $\Omega$-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in $\mathcal{N} = 4$ theory with $k$ fundamental hypermultiplets, having a holographic description as M-theory in the $\mathrm{AdS}_4 \times \mathrm{S}^7/\mathbb{Z}_k$ 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.