N=1 M5-brane geometries

TL;DR

The paper addresses constructing eleven-dimensional supergravity backgrounds dual to ${\mathcal N}=1$ gauge theories via M5-branes wrapped on holomorphic 2-cycles in $\mathbb{C}^3$. The authors develop a metric Ansatz with warp factors $H_1$, $H_2$ and a hermitian metric $G_{M\overline N}$ on the $\mathbb{C}^3$ directions, then derive BPS conditions from $\delta\Psi_i=0$ and relate the flux $F$ to geometric data. They reformulate the solution in terms of a rescaled metric $g_{M\overline N}=H^{-1/6} G_{M\overline N}$ and the hermitian 2-form $\omega=i g_{M\overline N} dz^M \wedge dz^{\overline N}$, showing that the constraint is $\omega^2$ being closed and the flux obeys $dF=J$ with a source $J$ for the wrapped cycle. This framework enables near-horizon duals for $\mathcal{N}=1$ theories, connects to $\mathcal{N}=2$ wrapped-brane constructions and Becker-Becker constraints, and highlights future directions including solving the source equation for explicit cycles and exploring warped-geometric phenomenology.

Abstract

We describe how to construct solutions to 11-dimensional supergravity corresponding to M5-branes wrapped on holomorphic 2-cycles embedded in C^3. These solutions preserve N=1 supersymmetry in four dimensions. In the near-horizon limit they are expected to be dual to N=1 large N gauge theories in four dimensions by Maldacena's duality.