M5-branes Probing Flux Backgrounds

TL;DR

This paper investigates the global symmetries and anomalies of 4d $ ext{N}=1$ theories from M5-branes probing flux backgrounds, extending known holographic duals and using anomaly inflow to analyze generalizations for higher flux quanta.

Contribution

It develops a systematic approach using anomaly inflow to analyze global symmetries and anomalies in M5-brane probe theories with flux backgrounds, including cases beyond known holographic solutions.

Findings

Identified continuous and discrete global symmetries via anomaly inflow.

Computed 't Hooft anomalies at large N limit.

Laid groundwork for analyzing general flux backgrounds for M5-branes.

Abstract

We analyze the global symmetries and anomalies of 4d $\mathcal{N} = 1$ field theories that arise from a stack of $N$ M5-branes probing a class of flux backgrounds. These backgrounds consist of a resolved $\mathbb{C}^2 / \mathbb{Z}_k$ singularity fibered over a smooth Riemann surface of genus $g \geq 2$, supported by a non-trivial $G_4$-flux configuration labeled by a collection of $2(k-1)$ flux quanta, $\{N_i\}$. For $k=2$, this setup defines a non-trivial superconformal field theory (SCFT) in the IR, which is holographically dual to an explicit $AdS_5$ solution first described by Gauntlett, Martelli, Sparks, and Waldram. The generalization to $k \geq 3$ is hard to tackle directly within holography. Instead, in this paper we lay the groundwork for a systematic analysis of such a generalization by adopting anomaly inflow methods to identify continuous and discrete global symmetries of the 4d field theories. We also compute the 't Hooft anomalies for continuous symmetries at leading order in the limit of large $N$, $N_i$.