Anomaly Inflow for M5-branes on Punctured Riemann Surfaces

TL;DR

This paper derives the anomaly polynomials of 4d N=2 theories from M5-branes on punctured Riemann surfaces using anomaly inflow in M-theory, providing a geometric top-down perspective that matches known results.

Contribution

It offers a top-down derivation of anomaly contributions for class S theories via M-theory anomaly inflow, complementing previous field-theoretic methods.

Findings

Derived anomaly polynomials for class S theories from M-theory.

Matched the results with known 4d N=2 SCFT anomaly polynomials.

Showed that boundary contributions are determined by G4-flux in 11d geometry.

Abstract

We derive the anomaly polynomials of 4d $\mathcal{N}=2$ theories that are obtained by wrapping M5-branes on a Riemann surface with arbitrary regular punctures, using anomaly inflow in the corresponding M-theory setup. Our results match the known anomaly polynomials for the 4d $\mathcal{N}=2$ class $\mathcal{S}$ SCFTs. In our approach, the contributions to the 't Hooft anomalies due to boundary conditions at the punctures are determined entirely by $G_4$-flux in the 11d geometry. This computation provides a top-down derivation of these contributions that utilizes the geometric definition of the field theories, complementing the previous field-theoretic arguments.