Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification

Kaidi, Justin; Zafrir, Gabi; Zheng, Yunqin

doi:10.48550/arxiv.2205.01104

Cited by 9 publications

(11 citation statements)

References 27 publications

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“…Compactification on these surfaces can be exploited to obtain class S theories with a Z (0) 4g+2 enhanced symmetries. 9 When φ is not a symmetry it can give rise to more interesting effects, that give rise to intrinsic K-ality defects in the language of [76]. There one obtains a theory with a non-invertible symmetry starting from this setup as well, by coupling the 4d theory to an appropriate SPT to compensate to the given transformation [62,79].…”

Section: D Origin Of Global Structure Of Class S Theoriesmentioning

confidence: 99%

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On the 6d Origin of Non-invertible Symmetries in 4d

Bashmakov¹,

Zotto²,

Hasan³

2022

Preprint

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It is well-known that six-dimensional superconformal field theories can be exploited to unravel interesting features of lower-dimensional theories obtained via compactifications. In this short note we discuss a new application of 6d (2,0) theories in constructing 4d theories with Kramers-Wannier-like non-invertible symmetries. Our methods allow to recover previously known results, as well as to exhibit infinitely many new examples of four dimensional theories with "M-ality" defects (arising from operations of order M generalizing dualities). In particular, we obtain examples of order M = p k , where p > 1 is a prime number and k is a positive integer.

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Section: D Origin Of Global Structure Of Class S Theoriesmentioning

confidence: 99%

“…In this paper we focus on cases that exhibit a mixed anomaly. In a follow up of this work we will study the more general case of intrinsic duality defects, building on uplifting the formalism introduced in [76] to our setup.…”

Section: Introductionmentioning

confidence: 99%

On the 6d Origin of Non-invertible Symmetries in 4d

Bashmakov¹,

Zotto²,

Hasan³

2022

Preprint

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“…In the past year, non-invertible symmetries have been constructed in many familiar continuum and lattice gauge theories in higher than two spacetime dimensions [30,31,29,[32][33][34][35][36]. These non-invertible symmetries are realized by gauging a higher-form global symmetry in either half of the spacetime [31,29,34,35], or on a higher-codimensional submanifold [32].…”

Section: Introductionmentioning

confidence: 99%

Non-invertible Global Symmetries in the Standard Model

Choi¹,

Lam²,

Shao³

2022

Preprint

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We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the U (1) A axial symmetry because of the ABJ anomaly, for every rational angle 2πp/N , we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic U (1) gauge field. These conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra over TQFT coefficients. They act invertibly on all local operators as axial rotations, but non-invertibly on the 't Hooft lines. These non-invertible symmetries lead to selection rules, which are consistent with the scattering amplitudes in QED. We further generalize our construction to QCD, and show that the coupling π 0 F ∧ F in the effective pion Lagrangian is necessary to match these non-invertible symmetries in the UV. Therefore, the conventional argument for the neutral pion decay using the ABJ anomaly is now rephrased as a matching condition of a generalized global symmetry.

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“…In 2+1d, the non-abelian anyons in a low-energy TQFT, described by the theory of modular tensor categories, can be viewed as the non-invertible generalization of one-form global symmetries (see [104][105][106][107]41] for recent discussions). Recently, the non-invertible Kramer-Wannier duality defects have been generalized to 3+1d gauge theories [108,109,102,110,47,111,112] via the gauging of higherform global symmetries. More generally, in any theory with a higher-form symmetry, the most fundamental non-invertible symmetries are condensation defects [42][43][44][45][46] arising from higher gauging [41].…”

Section: Non-invertible Symmetriesmentioning

confidence: 99%

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

Córdova¹,

Dumitrescu²,

Intriligator³

et al. 2022

Preprint

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Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow for new kinds of anomalies that constrain dynamics. We review some transformative instances of these novel aspects of symmetry in quantum field theory, and give a broad-brush overview of recent applications.

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Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification

Cited by 9 publications

References 27 publications

On the 6d Origin of Non-invertible Symmetries in 4d

On the 6d Origin of Non-invertible Symmetries in 4d

Non-invertible Global Symmetries in the Standard Model

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

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