Web of 4D Dualities, Supersymmetric Partition functions and SymTFT

TL;DR

This paper explores the role of symmetry topological field theories (SymTFT) in understanding 4D gauge theories with $ ext{Z}_N$ one-form symmetries, dualities, and supersymmetric protected quantities, providing new insights into their topological and duality structures.

Contribution

It introduces a SymTFT framework for analyzing 4D gauge theories with one-form symmetries, dualities, and supersymmetric invariants, offering a unified topological perspective.

Findings

Constructed topological boundary states on various 4-manifolds.

Revealed a web of 4D dualities within the SymTFT framework.

Extended SymTFT to include supersymmetric protected quantities.

Abstract

We study $\mathbb{Z}_N$ one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its canonical quantization and construct topological boundary states on several important classes of four manifolds that are spin, non-spin and torsional. We highlight a web of four-dimensional dualities, which can be naturally interpreted within the SymTFT framework. We also point out an intriguing class of four-dimensional gauge theories that exhibit mixed 't Hooft anomaly between one-form symmetries. In the second part of this work, we extend the SymTFT to account for various quantities protected by supersymmetry (SUSY) in SUSY gauge theories. We proposed that their behaviour under various symmetry operations are entirely captured by the topological boundary of the SymTFT, resulting in strong constraints. Concrete examples are considered, including the Witten index, the lens space index and the Donaldson-Witten and Vafa-Witten partition functions.