Gravity Dual of Two-Dimensional $\mathcal{N}=(2,2{)}^{\ast }$ Supersymmetric Yang-Mills Theory and Integrable Models

Abstract

The 2D $\mathcal{N}=(2,2{)}^{\ast }$ supersymmetric Yang-Mills theory can be obtained from the 2D $\mathcal{N}=(4,4)$ theory with a twisted mass deformation. In this paper we construct the gravity dual theory of the 2D $\mathcal{N}=(2,2{)}^{\ast }$ supersymmetric $U(N)$ Yang-Mills theory at the large $N$ and large 't Hooft coupling limit using the 5D gauged supergravity. In the UV regime, this construction also provides the gravity dual of the 2D $\mathcal{N}=(2,2{)}^{\ast }$ $U(N)$ topological Yang-Mills-Higgs theory. We propose a triality in the UV regime among integrable model, gauge theory and gravity, and we make some checks of this relation at classical level.

49 pages, 3 figures; V2: typos corrected, more discussions added

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• Modified non-linear Schrödinger models, $\mathcal{C}{\mathcal{P}}_s{\mathcal{T}}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges