Anomaly resolution via decomposition

Robbins, D.; Sharpe, E.; Vandermeulen, T.

doi:10.48550/arxiv.2107.13552

Cited by 5 publications

(6 citation statements)

References 18 publications

(51 reference statements)

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“…We find that when the SL(2, ℤ) bundle of the F-theory model is non-trivial, these models generically have a non-invertible symmetry simply because the fusion algebra for the generalized symmetry operators contains multiple summands. This is quite analogous to what has been observed in the context of various field theoretic constructions [14,38,43,44,55,56,62,64,65,74,[80][81][82]84,85,87,96,98,99,102,128,[131][132][133][134][135][136][137][138][139][140][141][142][143] as well as some recent holographic models. [100,101] We emphasize, however, that the construction we present can be applied to essentially any QFT which can be engineered via a string / M-/ F-theory compactification.…”

Section: Doi: 101002/prop202200180supporting

confidence: 80%

The Branes Behind Generalized Symmetry Operators

Heckman

Hübner

Torres

et al. 2022

Fortschritte der Physik

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The modern approach to m-form global symmetries in a d-dimensional quantum field theory (QFT) entails specifying dimension d − m − 1 topological generalized symmetry operators which non-trivially link with m-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry X, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary 𝝏X. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in 𝝏X. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

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Section: Doi: 101002/prop202200180supporting

confidence: 80%

The Branes Behind Generalized Symmetry Operators

Heckman

Hübner

Torres

et al. 2022

Fortschritte der Physik

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“…In this paper we focus on orbifolds with and without discrete torsion. Now, it was recently argued in [33][34][35] that two-dimensional orbifold in which a subgroup of the orbifold group acts trivially admit additional modular-invariant degrees of freedom, beyond discrete torsion, which were labelled "quantum symmetries." A version of decomposition for orbifolds with quantum symmetries was discussed in [33][34][35], and we leave further details of quantum symmetries to future work.…”

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confidence: 99%

“…There also exist more modular-invariant phases than just discrete torsion in the case a nontrivial subgroup of Γ acts trivially; see [33][34][35] for more information on such orbifolds and their corresponding decomposition. We leave such more general theories for future work.…”

mentioning

confidence: 99%

Topological operators, noninvertible symmetries and decomposition

Sharpe

2021

Preprint

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In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete torsion. As one component of our analysis, we study the ring of dimension-zero operators in two-dimensional theories exhibiting decomposition. From a commutative algebra perspective, the rings are naturally associated to a finite number of points, one point for each universe in the decomposition. Each universe is canonically associated to a representation, which defines a projector, an idempotent in the ring of dimension-zero operators. We discuss how Wilson lines on boundaries of two-dimensional theories decompose, and compute actions of projectors. We discuss one-form symmetries of the rings, and related properties. We also give general formulas for projection operators, which previously were computed on a case-by-case basis. Finally, we propose a characterization of noninvertible higher-form symmetries in this context in terms of representations. In that characterization, non-isomorphic universes appearing in decomposition are associated with noninvertible one-form symmetries. August 2021 D Miscellaneous group cohomology results 72 References 73

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“…For example, consider an orbifold [X/Γ], where a subgroup K ⊂ Γ acts trivially on X, as studied in e.g. [16][17][18][19][20][21][22][23][24]. This can be interpreted as a coupling of the orbifold [X/G] (for G = Γ/K) to Dijkgraaf-Witten theory for the group K, as will be discussed in greater detail in [25].…”

Section: A Basics Of Group Cohomology B Characters Of Projective Repr...mentioning

confidence: 99%

Combinatoric topological string theories and group theory algorithms

Ramgoolam¹,

Sharpe²

2022

Preprint

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A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for combinatoric topological strings (G-CTST) based on Dijkgraaf-Witten theory of flat G-bundles on surfaces. We extend this result to projective representations of G using twisted Dijkgraaf-Witten theory. New algorithms for characters are described, based on handle creation operators and minimal multiplicative generating subspaces for the centers of group algebras and twisted group algebras. Such minimal generating subspaces are of interest in connection with information theoretic aspects of the AdS/CFT correspondence. For the untwisted case, we describe the integrality properties of certain character sums and character power sums which follow from these constructive G-CTST algorithms. These integer sums appear as residues of singularities in G-CTST generating functions. S-duality of the combinatoric topological strings motivates the definition of an inverse handle creation operator in the centers of group algebras and twisted group algebras.

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Anomaly resolution via decomposition

Cited by 5 publications

References 18 publications

The Branes Behind Generalized Symmetry Operators

The Branes Behind Generalized Symmetry Operators

Topological operators, noninvertible symmetries and decomposition

Combinatoric topological string theories and group theory algorithms

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