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

Bashmakov, Vladimir; Zotto, Michele Del; Hasan, Azeem

doi:10.48550/arxiv.2206.07073

Cited by 8 publications

(12 citation statements)

References 50 publications

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“…Such defects may be non-invertible under fusion, and serve as an explicit construction of non-invertible symmetries in dimensions larger than two, which has seen a surge of interest very recently, see, e.g. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Decomposition, Condensation Defects, and Fusion

Robbins

Sharpe

2022

Fortschritte der Physik

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In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay with notions of decomposition, the statement that d-dimensional quantum field theories with global (d − 1)-form symmetries are equivalent to disjoint unions of other quantum field theories. We will also construct new (sometimes non-invertible) defects, and compute their fusion products, again utilizing decomposition. An important role will be played in all these analyses by theta angles for gauged higher-form symmetries, which can be used to select individual universes in a decomposition.

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Section: Introductionmentioning

confidence: 99%

Decomposition, Condensation Defects, and Fusion

Robbins

Sharpe

2022

Fortschritte der Physik

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“…These lines are coupled to the gauge field b ⊥ ≡ l T ⊥ T −1 B. 32 (We omit the dependence of t ⊥ and b ⊥ on T in order not to clutter.) We have then proved the factorization:…”

Section: Fusion On Gapped Boundariesmentioning

confidence: 99%

“…Extension to class S. Our formalism can naturally be extended to study self-duality noninvertible symmetries in other theories, for instance on the conformal manifold of N = 2 theories of class S (see [32] for related investigations). The symmetry TFT of the 6d N = (2, 0) theory of ADE type g is a 7d Chern-Simons theory of 3-form gauge fields with level matrix equal to the Cartan matrix A ij of g. After reducing on a genus-g Riemann surface Σ g , one obtains a 5d CS theory with 2g-tuples of 2-form gauge fields B i and braiding:…”

Section: Gapped Boundaries and Non-invertible Fusion Rulesmentioning

confidence: 99%

“…This structure is well understood for line operators in 2d quantum field theories (QFTs) and 3d topological quantum field theories (TQFTs) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] using the formalism of fusion categories and modular tensor categories. The generalization to higher dimensional defects and d > 2 QFTs started more recently with [20,21] and is now a very active field of research [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. At the moment we know of, roughly speaking, three types of constructions of non-invertible symmetry defects.…”

Section: Introductionmentioning

confidence: 99%

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The holography of non-invertible self-duality symmetries

Antinucci¹,

Benini²,

Copetti³

et al. 2022

Preprint

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We study how non-invertible self-duality defects arise in theories with a holographic dual. We focus on the paradigmatic example of su(N ) N = 4 SYM. The theory is known to have non-invertible duality and triality defects at τ = i and τ = e 2πi/3 , respectively. At these points in the gravitational moduli space, the gauged SL(2, Z) duality symmetry of type IIB string theory is spontaneously broken to a finite subgroup G, giving rise to a discrete emergent G gauge field. After reduction on the internal manifold, the low-energy physics is dominated by an interesting 5d Chern-Simons theory, further gauged by G, that we analyze and which gives rise to the self-duality defects in the boundary theory. Using the five-dimensional bulk theory, we compute the fusion rules of those defects in detail. The methods presented here are general and may be used to investigate such symmetries in other theories with a gravity dual.

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“…[5][6][7] The full physical impact of these symmetries is yet to be uncovered, but already numerous phenomenological and other applications have been studied. [8][9][10][11][12][13] All the above constructions rely crucially on gauging of global symmetries in theories with invertible, possibly generalized, symmetries, i.e. 0form or higher-form [14] or higher-group symmetries.…”

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

Cited by 8 publications

References 50 publications

Decomposition, Condensation Defects, and Fusion

Decomposition, Condensation Defects, and Fusion

The holography of non-invertible self-duality symmetries

Universal Non‐Invertible Symmetries

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