Fivebranes and 4-manifolds

TL;DR

This paper develops a framework connecting 4-manifolds with 2d N=(0,2) theories, leading to new insights into 3d N=2 theories, partition functions, and dualities via a novel dictionary and gluing rules.

Contribution

It introduces a new dictionary linking 4-manifold building blocks to 2d theories, resulting in novel 3d theories and interpretations of topological invariants and dualities.

Findings

New 3d N=2 theories T[M_3] for rational homology spheres

Relation between Vafa-Witten partition functions and 2d superconformal index

Interpretation of Kirby calculus as dualities of 2d and 3d theories

Abstract

We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which include new 3d N=2 theories T[M_3] associated with rational homology spheres and new results for Vafa-Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0,2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines / walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N=(0,2) theories and 3d N=2 theories, respectively