Speaker
Description
Line defects pose a fundamental challenge for dualities in gauge theories. While it is known that field theories with radically different gauge groups can be dual at low energies, it is not yet fully understood how the presence of a line defect in one theory maps in the dual description. This conundrum was partially solved in the case of 3d theories with N=4 supersymmetry related by mirror symmetry [1], where Wilson loops on one side of the duality were shown to be exchanged with 't Hooft loops in the dual theory [2]. Since mirror duality descends from the action of the S generator of the modular group SL(2,Z), it is natural to ask how line defects map across more general duality transformations within this group.
In this work, we provide a complete derivation of such a duality map in SL(2,Z) dual gauge theories. Remarkably, we adopt an entirely field-theoretic approach, thereby complementing previous results on S-duality obtained by means of brane arguments [2].
Our primary tool is the SL(2,Z) dualization algorithm [3]. This is a systematic procedure to derive SL(2,Z) duals by applying basic duality moves locally to the quiver constituents, proven on pure field theory grounds. The first preliminary result of this work is the extension of this algorithm to include the dualization of line operators. With this tool, we are able to determine how loop operators are dualized into each other when passing through a duality wall, be it associated with the S or T generator of SL(2,Z).
We then reproduce all the results of [2], including the derivation of a microscopic description of 't Hooft loops as coupled 1d/3d system, and provide a field theory interpretation of the manipulations performed at the level of the brane setup. Finally, we present an SL(2,Z) duality web between gauge theories endowed with codimension-two defects. All our results show perfect agreement with the structure predicted by brane constructions.
[1] K. A. Intriligator and N. Seiberg, “Mirror symmetry in three-dimensional gauge theories,” Phys. Lett. B 387 (1996) 513–519, arXiv:hep-th/9607207.
[2] B. Assel and J. Gomis, “Mirror Symmetry And Loop Operators,” JHEP 11 (2015) 055, arXiv:1506.01718 [hep-th].
[3] R. Comi, C. Hwang, F. Marino, S. Pasquetti, and M. Sacchi, “The SL(2, Z) dualization algorithm at work,” JHEP 06 (2023) 119, arXiv:2212.10571 [hep-th].