Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Hayashi, Yui; Tanizaki, Yuya

doi:10.48550/arxiv.2204.07440

Cited by 10 publications

(12 citation statements)

References 43 publications

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“…The triality fusion rules above can be viewed as the generalization of those in 1+1d [20,21]. Examples of similar triality defect fusion rules have recently been explored in U (1) lattice gauge theory [69]. Interestingly, the fusion "coefficients" between these topological defects can either be a 2+1d TQFT such as the twisted Z N gauge theory (Z N ) K or the SU (N ) −1 Chern-Simons theory, or a 2+1d SPT such as (−1) Q(M,Σ) .…”

mentioning

confidence: 94%

Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions

Choi¹,

Córdova²,

Hsin³

et al. 2022

Preprint

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We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, Z N gauge theories, and U (1) N Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, N = 1, and N = 4 super Yang-Mills theories.

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confidence: 94%

Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions

Choi¹,

Córdova²,

Hsin³

et al. 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]. The operators D p N in QED in this paper are realized from generalizations of such gauging constructions.…”

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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“…A similar structure was proposed later as a phenomenological explanation of the superuniversality of quantum Hall transitions in twodimensional electron fluids in large magnetic fields [29][30][31]. Although it has since been understood [32][33][34] that oblique confining phases of the Cardy-Rabinovici (CR) model possess anyonic braiding of point charges with vortex lines-and thus topological order-a detailed understanding of the precise topological order, boundary states, and topological response for a generic oblique confining phase has been lacking.…”

Section: Introductionmentioning

confidence: 82%

Theory of oblique topological insulators

Benjamin¹,

Goldman²,

Sohal³

et al. 2022

Preprint

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A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional Θ-angles, long-range entanglement, and fractionalization. Starting from a simple family of Z N lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons-bound states of electric charges and monopoles-condense, leading to FTI phases characterized by topological order, emergent one-form symmetries, and gapped boundary states not realizable in 2+1-D alone. Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal "generalized magnetoelectric effect" in the presence of two-form background gauge fields. Moreover, we characterize the possible boundary topological orders of oblique TIs, finding a new set of boundary states not studied previously for these kinds of TQFTs.

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Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Cited by 10 publications

References 43 publications

Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions

Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions

Non-invertible Global Symmetries in the Standard Model

Theory of oblique topological insulators

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