Non-invertible symmetries of $$ \mathcal{N} $$ = 4 SYM and twisted compactification

Kaidi, Justin; Zafrir, Gabi; Zheng, Yunqin

doi:10.1007/jhep08(2022)053

Cited by 69 publications

(57 citation statements)

References 49 publications

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“…[ 5–8 ] A number of recent works have shown that symmetry operators without inverses (and which are therefore not elements of any group, but should rather be thought of in categorical terms) are also very common in higher dimensional theories. [ 9–26 ] In this paper we will focus on one class of theories where such non‐invertible symmetries appear:

\mathcal {N}=4

theories with gauge group

\mathrm{Pin}^+(4N)

Sc(4N)

and

PO(4N)

. [ 14 ] The details are a little different in the three cases, so in this introduction we will focus on the

Sc(4N)

case for concreteness.…”

Section: Introductionmentioning

confidence: 99%

Branes and Non‐Invertible Symmetries

García-Etxebarria

2022

Fortschritte der Physik

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\mathcal {N}=4

theories with gauge group

\mathrm{Pin}^+(4N)

Sc(4N)

and

PO(4N)

. [ 14 ] The details are a little different in the three cases, so in this introduction we will focus on the

Sc(4N)

case for concreteness.…”

Section: Introductionmentioning

confidence: 99%

Branes and Non‐Invertible Symmetries

García-Etxebarria

2022

Fortschritte der Physik

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“…In some cases we can see from the index of the resulting theory that the additional gauging of a zero-form symmetry is obstructed, thus indicating the presence of the mixed anomaly in the original theory. As it was pointed out in [37,43,45], if the resulting anomaly takes a suitable form, then it leads to interesting consequences after gauging. In particular, if we gauge the two zero-form symmetries in the original theory, the remaining one-form symmetry is noninvertible.…”

Section: Introductionmentioning

confidence: 86%

Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices

Mekareeya,

Sacchi

2022

Preprint

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Mixed anomalies, higher form symmetries, two-group symmetries and noninvertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete zero-form global symmetries, and possibly a one-form symmetry, in 3d N ≥ 3 gauge theories using the superconformal index. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, such as the U(1) k gauge theory with hypermultiplets of diverse charges, the T (SU(N )) theory of Gaiotto-Witten, the theories with so(2N ) 2k gauge algebra and hypermultiplets in the vector representation, and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries of some of these models, we obtain various interesting theories with non-invertible symmetries or two-group structures.

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“…[ 5–7 ] The full physical impact of these symmetries is yet to be uncovered, but already numerous phenomenological and other applications have been studied. [ 8–13 ]…”

Section: Introductionmentioning

confidence: 99%

Universal Non‐Invertible Symmetries

Bhardwaj

Schäfer‐Nameki

2022

Fortschritte der Physik

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It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a 1-category. We argue that for a d-dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a (d − 1)-category, which is formed out of lower-dimensional topological quantum field theories with the same 0-form symmetry. We study in detail a 2-categorical piece of this (d − 1)-category described by 2d topological quantum field theories with 0-form symmetry. We further show that the objects of this 2-category are the recently discussed 2d condensation defects constructed from higher-gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher-form or higher-group symmetry also form a (d − 1)-category formed out of lower-dimensional topological quantum field theories with that higher-form or higher-group symmetry. A particularly interesting case is that of the 2-category of dual symmetries associated to gauging of finite 2-group symmetries, as it describes non-invertible symmetries arising from gauging 0-form symmetries that act on (d − 3)-form symmetries. Such non-invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non-invertible symmetries. We describe how our results can be applied to compute non-invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2-category formed by 2d condensation defects in any arbitrary quantum field theory.

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Non-invertible symmetries of $$ \mathcal{N} $$ = 4 SYM and twisted compactification

Cited by 69 publications

References 49 publications

Branes and Non‐Invertible Symmetries

Branes and Non‐Invertible Symmetries

Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices

Universal Non‐Invertible Symmetries

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