Anomalies and Graded Coisotropic Branes

TL;DR

This paper investigates the anomaly conditions of coisotropic branes in the A-model on Calabi-Yau manifolds, establishing a link between anomaly freedom and gradability of these branes.

Contribution

It demonstrates that coisotropic branes are anomaly-free if and only if they are graded, connecting anomaly conditions with recent definitions of graded coisotropic branes.

Findings

Anomaly-free condition is equivalent to gradability of coisotropic branes.

Provides a relation between anomalies and recent grading concepts.

Comments on alternative grading approaches for coisotropic submanifolds.

Abstract

We compute the anomaly of the axial U(1) current in the A-model on a Calabi-Yau manifold, in the presence of coisotropic branes discovered by Kapustin and Orlov. Our results relate the anomaly-free condition to a recently proposed definition of graded coisotropic branes in Calabi-Yau manifolds. More specifically, we find that a coisotropic brane is anomaly-free if and only if it is gradable. We also comment on a different grading for coisotropic submanifolds introduced recently by Oh.