Cornering Relative Symmetry Theories

Abstract

The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated $(d+1)$-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in $D=d+m$ dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, with the original QFT degrees of freedom localized at a corner of this $D$-dimensional bulk system. We present a bottom up characterization of this structure and also show how it naturally arises in a number of string-based constructions of QFTs with both finite and continuous symmetries.

105 pages, 22 figures

Cited by in corpus (4)

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• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond