Coisotropic Branes in Toric Calabi-Yau 3-folds

TL;DR

This paper investigates coisotropic branes in toric Calabi-Yau 3-folds, revealing that disk multi-cover formulas match those for Lagrangian branes and exploring their role as surface defects in gauge theories.

Contribution

It introduces the study of coisotropic branes in toric Calabi-Yau 3-folds, demonstrating their disk-instanton properties and their application as surface defects in geometric engineering.

Findings

Disk multi-cover formulas are identical to those for Lagrangian branes.

Fermion zero modes are identified on disks ending on coisotropic branes.

Coisotropic branes can serve as surface defects in 4d N=2 SU(K) gauge theories.

Abstract

We study disk-instantons ending on coisotropic branes preserved by real torus action in toric Calabi-Yau 3-folds. In particular, we find fermion zero modes on disk multi-covers ending on a coisotropic brane in local P^1 geometry with normal bundle (-a,a-2). It turns out that, independent of a, disk multi-cover formula is the same as for disks ending on a Lagrangian brane in resolved conifold. We further construct an example of a coisotropic brane in Calabi-Yau 3-fold used in geometric engineering of 4d N=2 SU(K) gauge theory, where this brane provides a surface defect.