Top down approach to topological duality defects
Jonathan J. Heckman, Max Hübner, Ethan Torres, Xingyang Yu, Hao Y. Zhang
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 noninvertible 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. Nontrivial 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 $\ensuremath{\partial}X$ results in a 5D symmetry topological field theory. 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.