SymTFT Fans: The Symmetry Theory of 4d N=4 Super Yang-Mills on spaces with boundaries

TL;DR

This paper explores the SymTFT construction for 4d N=4 Super Yang-Mills with boundaries, revealing a fan-like structure of sectors connected by gapless interfaces, advancing understanding of symmetries in boundary quantum field theories.

Contribution

It introduces the SymTFT framework for boundary theories, specifically analyzing the complex fan-like structure in 4d N=4 Super Yang-Mills with Gaiotto-Witten boundary conditions.

Findings

Discovery of a fan-like SymTFT structure with multiple sectors

Identification of gapless interfaces merging at boundary SCFT

Enhanced understanding of boundary symmetries in 4d gauge theories

Abstract

The SymTFT construction is an efficient way of studying the symmetries of Quantum Field Theories. In this paper we initiate the study of the SymTFT construction for interacting theories on spaces with boundaries, in the concrete example of $d = 4$ $\mathcal{N} = 4$ Super Yang-Mills theory with Gaiotto-Witten boundary conditions. The resulting SymTFT has a number of peculiarities, most prominently a fan-like structure with a number of different SymTFT sectors joined by gapless interfaces that merge at the Gaiotto-Witten boundary SCFT.