Vortex counting from field theory

TL;DR

This paper derives the vortex partition function in 2d N=(2,2) U(N) gauge theory using the moduli matrix approach and localization, highlighting the importance of fermionic zero modes and exploring orbifold cases.

Contribution

It introduces a field theoretical derivation of the vortex partition function incorporating matter fields and orbifold cases, emphasizing the role of fermionic zero modes.

Findings

Derived vortex partition function using localization and moduli matrix.

Highlighted the importance of fermionic zero modes for matter fields.

Explored orbifold vortex partition functions from a field theory perspective.

Abstract

The vortex partition function in 2d N = (2,2) U(N) gauge theory is derived from the field theoretical point of view by using the moduli matrix approach. The character for the tangent space at each moduli space fixed point is written in terms of the moduli matrix, and then the vortex partition function is obtained by applying the localization formula. We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets. The orbifold vortex partition function is also investigated from the field theoretical point of view.