M5-brane Sources, Holography, and Argyres-Douglas Theories

TL;DR

This paper constructs holographic duals for a class of 4d $ ext{N}=2$ superconformal theories, including Argyres-Douglas theories, using M5-branes and 7d supergravity, and verifies the duality through multiple consistency checks.

Contribution

It introduces new holographic solutions with M5-brane sources for Argyres-Douglas theories, featuring a novel supersymmetry realization and anomaly computations.

Findings

Holographic central charge matches field theory predictions.

Flavor symmetry central charge computed holographically.

Dimensions of supersymmetric probe M2-branes agree with dual theories.

Abstract

We initiate a study of the holographic duals of a class of four-dimensional $\mathcal{N}=2$ superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of $AdS_5$ and a "half-spindle." The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting St\"uckelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large-$N$ 't Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality.