Modified Villain lattice realizations of flat-gauged interfaces and T-duality defects in the 2D compact boson are constructed at arbitrary radii, yielding non-compact edge modes with continuous spectrum and infinite quantum dimension.
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Generalized Global Symmetries
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A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
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- abstract A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either complete
- method metriesingeometricengineeringconstructionsofquantumfieldtheoriesviastringtheory, and the study of higher-form symmetries using holographic duality. 2 Introduction to Higher-Form Symmetries The aim of this section is to introducep-form symmetries. These symmetries generalize the usual global symmetries, which in this language are referred to as 0-form symmetries. We will follow the seminal work [4], though this is not to say that this was the first work discussing such ideas. In fact, many of the
- background Somewhat later, a seemingly unrelated-at the time (see the last paragraph in this Section)-development was inspired by the work of Ünsal from 2007 [9, 10]. He showed that objects of fractional topological charge were behind semiclassical confinement and chiral symmetry breaking onR3 ×S 1. The fractionally-charged objects are the so-called "monopole- instantons;" see the review [11] for an extensive list of references. The more recent interest in the subject was driven by the improved understandi
- background While defects are rich subjects of study in their own right, they also serve as powerful tools to understand the quantum field theories in which they are embedded. In particular, we note that certain defects can be continuously deformed without affecting any physical observables. These are topological defects, which generalize the very notion of symmetry in modern physics [1, 2]. This perspective has shed new light on many profound phenomena in quantum field theories, and we will apply it extens
- background 4 The combination U(1)B−L is exactly preserved in the SM, but is expected to be violated by physics beyond the SM (BSM). 5 These are symmetric tensors of the Lorentz group with s≥ 3 indices. By contrast, the stress tensor Tµν is a two-index Lorentz tensor of spin s = 2. 6 A CFT analogue of the CM theorem was proved in [16]. 7 We sometimes call U (0)(g, Σd−1) a symmetry defect. For an exposition of this perspective, see for instance [21] and refer- ences therein. Throughout we use X (p) to indica
- background Verstraete,Anyons and matrix product operator algebras,Annals Phys. 378(2017) 183-233, arXiv:1511.08090 [cond-mat.str-el]. [41] R. Vanhove, M. Bal, D. J. Williamson, N. Bultinck, J. Haegeman, and F. Verstraete,Mapping topological to conformal field theories through strange correlators, Phys. Rev. Lett.121(2018) 177203, arXiv:1801.05959 [quant-ph]. [42] K. Inamura,Topological field theories and symmetry protected topological phases with fusion category symmetries,Journal of High Energy Physics202
- background Alternatively, it is sourced by a localizedG-flux (fractional, in the discrete case). 1 Introduction The space of defects in a quantum system has been the subject of intense recent study: defects arise naturally as impurities in condensed-matter setups, and serve as probes of strongly coupled bulk dy- namics. Topological defects in particular - i.e. symmetries [1] - have led to a wealth of constraints on the long-distance physics, and their classification across dimensions has reached an increas
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Lattice Realizations of Flat Gauging and T-duality Defects at Any Radius
Modified Villain lattice realizations of flat-gauged interfaces and T-duality defects in the 2D compact boson are constructed at arbitrary radii, yielding non-compact edge modes with continuous spectrum and infinite quantum dimension.
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Non-Invertible Anyon Condensation and Level-Rank Dualities
New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
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Non-Invertible Duality Defects in 3+1 Dimensions
Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.
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Half-BPS Boundaries and the RG-Wall of $\mathcal{N}=2$ $SU(N)$ SYM
A massive deformation of the T[SU(N)] theory is identified as the 3d SCFT realizing the RG-wall and half-BPS boundaries in 4d N=2 SU(N) SYM.
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Non-relativistic limits of $\mathcal N=4$ supersymmetric Yang-Mills theory and S-duality
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Monopoles, Center Vortices, Confinement in (3+1)d, and the Lens-Space Twisted Partition Function
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On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies
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Defect Conformal Manifolds along RG Domain Walls between $\mathbb Z_N$-Parafermions and Minimal Models
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Stringy T-duality on the lattice and the twisted Villain model
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