Vertex algebras and 4-manifold invariants

TL;DR

This paper introduces a novel approach to computing 4-manifold invariants using chiral correlation functions in half-twisted 2D theories derived from fivebrane compactifications, offering new insights into Seiberg-Witten invariants.

Contribution

It provides a new theoretical framework connecting 4-manifold invariants with 2D supersymmetric theories, offering reinterpretations and predictions for invariants.

Findings

Reinterprets Seiberg-Witten invariants through 2D theories

Predicts structural properties of multi-monopole invariants

Suggests non-abelian generalizations of known invariants

Abstract

We propose a way of computing 4-manifold invariants, old and new, as chiral correlation functions in half-twisted 2d $\mathcal{N}=(0,2)$ theories that arise from compactification of fivebranes. Such formulation gives a new interpretation of some known statements about Seiberg-Witten invariants, such as the basic class condition, and gives a prediction for structural properties of the multi-monopole invariants and their non-abelian generalizations.