Topological Field Theory Amplitudes for $A_{N-1}$ Fibration

TL;DR

This paper establishes a connection between 5D supersymmetric gauge theory partition functions and two-dimensional topological field theories, revealing a new geometric interpretation involving Calabi-Yau threefolds and Lagrangian branes.

Contribution

It demonstrates that the partition function of 5D $U(N)$ gauge theory with massless adjoint hypermultiplets equals a 2D topological field theory amplitude, providing a novel geometric perspective.

Findings

Partition function matches 2D topological field theory amplitudes.

Topological amplitudes correspond to open string amplitudes with Lagrangian branes.

Provides a geometric interpretation involving Calabi-Yau threefolds.

Abstract

We study the partition function ${\cal N}=1$ 5D $U(N)$ gauge theory with $g$ adjoint hypermultiplets and show that for massless adjoint hypermultiplets it is equal to the partition function of a two dimensional topological field on a genus $g$ Riemann surface. We describe the topological field theory by its amplitudes associated with cap, propagator and pair of pants. These basic amplitudes are open topological string amplitudes associated with certain Calabi-Yau threefolds in the presence of Lagrangian branes.