Treelike structure of symmetry topological field theories and multisector QFTs
Florent Baume, Jonathan J. Heckman, Max Hübner, Ethan Torres, Andrew P. Turner, Xingyang Yu
Abstract
The global symmetries 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, in many cases, be captured in terms of a (<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 symmetry topological field theory (SymTFT). In this work we construct a (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>D</e:mi><e:mo>+</e:mo><e:mn>1</e:mn></e:mrow></e:math>)-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>M</g:mi></g:math> averaging where the topological sectors of different large <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>M</i:mi></i:math> replicas become dressed by additional extended operators associated with the SymTree. Published by the American Physical Society 2024