4d $\mathcal{N} = 1$/2d Yang-Mills Duality in Holography

TL;DR

This paper establishes a holographic duality connecting 4d $ abla=1$ superconformal theories from wrapped M5-branes to 2d Yang-Mills theory on a Riemann surface, via an effective 3d supergravity description.

Contribution

It derives an effective three-dimensional supergravity theory that links 4d superconformal field theories to 2d Yang-Mills theory through holography.

Findings

Effective 3d theory describes RG flows between AdS$_7$ and AdS$_5$.

Reduction to 2d $SU(2)$ Yang-Mills on the Riemann surface.

Holographic correspondence between M5-brane theories and 2d Yang-Mills.

Abstract

We study the supergravity dual of four-dimensional ${\mathcal{N}=1}$ superconformal field theories arising from wrapping M5-branes on a K\"ahler two-cycle inside a Calabi-Yau threefold. We derive an effective three-dimensional theory living on the cobordism between the infrared and ultraviolet Riemann surfaces, describing the renormalization group flows between AdS$_7$ and AdS$_{5}$ as well as between different AdS$_{5}$ fixed points. The realization of this system as an effective theory is convenient to make connections to known theories, and we show that upon imposing (physical) infrared boundary conditions, the effective three-dimensional theory further reduces to two-dimensional $SU(2)$ Yang-Mills theory on the Riemann surface, thus deriving a correspondence between the gravity duals of a class of $\mathcal{N}=1$ superconformal field theories arising from wrapping M5-branes on a Riemann surface and two-dimensional Yang-Mills theory on the same Riemann surface.