Intermediate defect groups, polarization pairs, and noninvertible duality defects

Abstract

Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing noninvertible duality defects in theories in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mi>k</a:mi></a:mrow></a:math> spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>k</c:mi><c:mo>−</c:mo><c:mn>1</c:mn></c:mrow></c:math>)-form defect groups are concerned, including their (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>k</e:mi><e:mo>−</e:mo><e:mn>1</e:mn></e:mrow></e:math>)-form symmetries, global structures (including discrete <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>θ</g:mi></g:math>-angle), and local counterterms. Using the associated symmetry topological field theory (TFT), we show that the polarization pair is capable of succinctly describing topological manipulations, e.g., gauging (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>k</i:mi><i:mo>−</i:mo><i:mn>1</i:mn></i:mrow></i:math>)-form global symmetries and stacking counterterms, of absolute QFTs. Furthermore, automorphisms of the (<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>k</k:mi><k:mo>−</k:mo><k:mn>1</k:mn></k:mrow></k:math>)-form charge lattice naturally act on polarization pairs via their action on the defect group; they can be viewed as dualities between absolute QFTs descending from the same relative QFT. Using this formalism, we present a prescription for building noninvertible symmetries of absolute QFTs. A large class of known examples, e.g., noninvertible defects in 4D <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="script">N</m:mi><m:mo>=</m:mo><m:mn>4</m:mn></m:math> super-Yang-Mills, can be reformulated via this prescription. As another class of examples, we identify and investigate in detail a family of noninvertible duality defects in 6D superconformal field theories (SCFTs), including from the perspective of the symmetry TFT derived from type IIB string theory. Published by the American Physical Society 2024

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