Cornering relative symmetry theories
Mirjam Cvetič, Ron Donagi, Jonathan J. Heckman, Max Hübner, Ethan Torres
Abstract
The symmetry data of a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>d</a:mi> </a:math> -dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory. 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 ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>d</c:mi> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> )-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>D</e:mi> <e:mo>=</e:mo> <e:mi>d</e:mi> <e:mo>+</e:mo> <e:mi>m</e:mi> </e:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>D</g:mi> </g:math> -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.