Non-invertible duality defect and non-commutative fusion algebra

We study non-invertible duality symmetries by gauging a diagonal subgroup of a non-anomalous U(1) \(\times\) U(1) global symmetry. In particular, we employ the half-space gauging to \(c=2\) bosonic torus conformal field theory (CFT) in two dimensions and pure U(1) \(\times\) U(1) gauge theory in fou...

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Bibliographic Details
Published inarXiv.org
Main Authors Nagoya, Yuta, Shimamori, Soichiro
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.01.2024
Subjects
Defects
Field theory
Gaging
Gauge theory
Half spaces
Subgroups
Symmetry
Toruses
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Summary:We study non-invertible duality symmetries by gauging a diagonal subgroup of a non-anomalous U(1) \(\times\) U(1) global symmetry. In particular, we employ the half-space gauging to \(c=2\) bosonic torus conformal field theory (CFT) in two dimensions and pure U(1) \(\times\) U(1) gauge theory in four dimensions. In \(c=2\) bosonic torus CFT, we show that the non-invertible symmetry obtained from the diagonal gauging becomes emergent on an irrational CFT point. We also calculate the fusion rules concerning the duality defect. We find out that the fusion algebra is non-commutative. We also obtain a similar result in pure U(1) \(\times\) U(1) gauge theory in four dimensions.
ISSN:2331-8422