Generalized charges, part I: Invertible symmetries and higher representations

Bhardwaj, Lakshya; Schäfer-Nameki, Sakura

doi:10.21468/scipostphys.16.4.093

Cited by 17 publications

(2 citation statements)

References 72 publications

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“…Another interesting development is triggered by study of topological defects in ddimensional CFT [38][39][40][41][42][43][44][45][46][47][48]. The defects are extended states in the CFT, generated by line operators or surface operators, etc.…”

Section: Introductionmentioning

confidence: 99%

Duality defects in Dn-type Niemeier lattice CFTs

Grover,

Hegde,

Jatkar

2024

J. High Energ. Phys.

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We discuss the construction of duality defects in c = 24 meromorphic CFTs that correspond to Niemeier lattices. We will illustrate our constructions for the Dn-type lattices. We will identify non-anomalous ℤ2 symmetries of these theories, and we show that on orbifolding with respect to these symmetries, these theories map to each other. We investigate this map, and in the case of self-dual orbifolds, we provide the duality defect partition functions. We show that exchange automorphisms in some CFTs give rise to a new class of defect partition functions.

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Section: Introductionmentioning

confidence: 99%

Duality defects in Dn-type Niemeier lattice CFTs

Grover,

Hegde,

Jatkar

2024

J. High Energ. Phys.

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“…While order parameters of ordinary symmetries are local fields [24], order parameters of n-form symmetries are n-brane fields [22,23]. 2 An n-form symmetry is a generalized symmetry [25][26][27][28] whose symmetry defects are codimension (n + 1) and whose symmetry charges are carried by ≥ n dimensional objects [29][30][31][32][33][34][35][36][37]. Therefore, classifying topological solitons of brane fields also classifies solitons associated with higher-form symmetries.…”

Section: Introductionmentioning

confidence: 99%

Topological aspects of brane fields: Solitons and higher-form symmetries

Pace,

Liu

2024

SciPost Phys.

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In this note, we classify topological solitons of n-brane fields, which are nonlocal fields that describe n-dimensional extended objects. We consider a class of n-brane fields that formally define a homomorphism from the n-fold loop space \Omega^n X_DΩnXD of spacetime X_DXD to a space Ε_nΕn. Examples of such n-brane fields are Wilson operators in n-form gauge theories. The solitons are singularities of the n-brane field, and we classify them using the homotopy theory of E_nEn-algebras. We find that the classification of codimension {k+1}k+1 topological solitons with {k≥ n}k≥n can be understood using homotopy groups of \mathcal{E}_nℰn. In particular, they are classified by {\pi_{k-n}(\mathcal{E}_n)}πk−n(ℰn) when {n>1}n>1 and by {\pi_{k-n}(\mathcal{E}_n)}πk−n(ℰn) modulo a {\pi_{1-n}(\mathcal{E}_n)}π1−n(ℰn) action when {n=0}n=0 or {1}1. However, for {n>2}n>2, their classification goes beyond the homotopy groups of \mathcal{E}_nℰn when k < n, which we explore through examples. We compare this classification to n-form \mathcal{E}_nℰn gauge theory. We then apply this classification and consider an {n}n-form symmetry described by the abelian group {G^{(n)}}G(n) that is spontaneously broken to {H^{(n)}\subset G^{(n)}}H(n)⊂G(n), for which the order parameter characterizing this symmetry breaking pattern is an {n}n-brane field with target space {\mathcal{E}_n = G^{(n)}/H^{(n)}}ℰn=G(n)/H(n). We discuss this classification in the context of many examples, both with and without ’t Hooft anomalies.

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Holographic Duals of Symmetry Broken Phases

Antinucci,

Benini,

Rizi

2024

Fortschritte der Physik

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A novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of gravity is explored by proposing a holographic duality where the bulk SymTFT (with the gauging of a suitable Lagrangian algebra) is dual to the universal effective field theory (EFT) that describes spontaneous symmetry breaking on the boundary. The authors tested this conjecture in various dimensions and with many examples involving different continuous symmetry structures, including non‐Abelian and non‐invertible symmetries, as well as higher groups. For instance, many Abelian SymTFTs are found to be dual to free theories of Goldstone bosons or generalized Maxwell fields, while non‐Abelian SymTFTs relate to non‐linear sigma models with target spaces defined by the symmetry groups. The analysis is also extended to include the non‐invertible axial symmetry, which is shown to be dual to axion‐Maxwell theory, and a non‐Abelian 2‐group structure in four dimensions, deriving a new parity‐violating interaction that has implications for the low‐energy dynamics of QCD.

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Generalized charges, part I: Invertible symmetries and higher representations

Cited by 17 publications

References 72 publications

Duality defects in Dn-type Niemeier lattice CFTs

Duality defects in Dn-type Niemeier lattice CFTs

Topological aspects of brane fields: Solitons and higher-form symmetries

Holographic Duals of Symmetry Broken Phases

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