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arXiv · 2402.00118

On the Fate of Stringy Non-Invertible Symmetries

Jonathan J. Heckman·Jacob McNamara·Miguel Montero·Adar Sharon·Cumrun Vafa·Irene Valenzuela
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Abstract

Non-invertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of non-invertible gauge symmetries? In theories with gravity we find a new form of non-invertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy non-invertible gauge symmetries appear in standard examples such as non-abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of non-invertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate non-invertible symmetries have implications for Swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the Distance Conjecture, and can sometimes explain the existence of slightly sub-extremal states which fill in the gaps in the sublattice Weak Gravity Conjecture.

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Jonathan J. Heckman, Jacob McNamara, Miguel Montero, Adar Sharon, Cumrun Vafa, Irene Valenzuela. 2024-01-31. On the Fate of Stringy Non-Invertible Symmetries. https://arxiv.org/abs/2402.00118

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