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

Abstract

We study the supergravity dual of four-dimensional $\mathcal{N}=1$ superconformal field theories arising from wrapping M5-branes on a Kähler 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.

18 pages, 2 figures; v2: clarifications added, slight extension to non-constant curvature metrics in UV, published version

References in corpus (5)

• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Four-Dimensional SCFTs from M5-Branes
• Branes, Calibrations and Supergravity
• AdS5 solutions from M5-branes on Riemann surface and D6-branes sources
• Kähler Uniformization from Holographic Renormalization Group Flows of M5-branes

Cited by in corpus (3)

• A slow review of the AGT correspondence
• Wrapped Branes and Punctured Horizons
• Holographic Uniformization and Black Hole Attractors