Top Down Approach to Topological Duality Defects

TL;DR

This paper develops a top-down method to construct topological duality defects in quantum field theories, extending previous work in supersymmetric theories to more general cases using string theory setups involving D3-branes and Calabi-Yau singularities.

Contribution

It introduces a top-down construction of duality defects applicable to QFTs with lower supersymmetry, utilizing D3-branes probing Calabi-Yau cones and string dualities.

Findings

Constructs duality defects via D-brane configurations and string dualities.

Shows how different defect realizations correspond to choices of branch cuts in the bulk.

Extends the understanding of non-invertible symmetries in various QFTs.

Abstract

Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D $\mathcal{N} = 4$ Super Yang-Mills (SYM) theory, an appropriate choice of (complexified) gauge coupling and global form of the gauge group can lead to a rather rich fusion algebra for the associated defects, leading to examples of non-invertible symmetries. In this work we present a top down construction of these duality defects which generalizes to QFTs with lower supersymmetry, where other 0-form symmetries are often present. We realize the QFTs of interest via D3-branes probing $X$ a Calabi-Yau threefold cone with an isolated singularity at the tip of the cone. The IIB duality group descends to dualities of the 4D worldvolume theory. Non-trivial codimension one topological interfaces arise from configurations of 7-branes "at infinity" which implement a suitable $SL(2, \mathbb{Z})$ transformation when they are crossed. Reduction on the boundary topology $\partial X$ results in a 5D symmetry TFT. Different realizations of duality defects, such as the gauging of 1-form symmetries with certain mixed anomalies and half-space gauging constructions, simply amount to distinct choices of where to place the branch cuts in the 5D bulk.