Supergravity M5-branes wrapped on Riemann surfaces and their QFT duals

TL;DR

The paper constructs new 11D supergravity solutions describing M5-branes wrapped on holomorphic Riemann surfaces, yielding gravity duals of ${\cal N}=2$ gauge theories, including non-conformal cases. By decomposing the Kähler potential into two holomorphic-dependent parts and enforcing a determinant constraint, it provides a systematic method to obtain the dual geometry from a Seiberg-Witten curve, with $F=f^{1/N}$ for a curve defined by $f(w,y)=0$. In the explicit SU($N$) Yang-Mills example, the curve $f=e^{y}+2B(w)+e^{-y}=0$ leads to an integral expression for an auxiliary function $h(f,w)$ and ties gauge-theory moduli to the gravity solution via the coefficients of $B(w)$. This framework offers a path to classify geometries dual to ${\cal N}=2$ theories and to study their RG flows and large-$N$ limits holographically.

Abstract

We find solutions of 11-dimensional supergravity for M5-branes wrapped on Riemann surfaces. These solutions preserve ${\cal N} = 2$ four-dimensional supersymmetry. They are dual to ${\cal N} = 2$ gauge theories, including non-conformal field theories. We work out the case of ${\cal N} = 2$ Yang-Mills in detail.