Anomaly inflow for M5-branes on punctured Riemann surfaces

Abstract

A bstract We derive the anomaly polynomials of 4d $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> 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 $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> class 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.