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.
hub Canonical reference
Generalized Global Symmetries
Canonical reference. 93% of citing Pith papers cite this work as background.
83
Pith papers citing it
Background
93% of classified citations
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 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.
hub tools
citation-role summary
background 42
method 3
citation-polarity summary
claims ledger
- 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
co-cited works
representative citing papers
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
A derived-geometric definition of p-form connections on infinity-bundles is given via splittings of the Atiyah L-infinity-algebroid, recovering Cech-Deligne cocycles for higher U(1)-bundles.
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.
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.
Constructs a family of non-relativistic limits of 4d MSYM via brane setups that organize into a 3D moduli space with nontrivial topology where PSL(2,Z) dualities act more complexly than in the relativistic theory, establishing Abelian duality by path integral and supporting non-Abelian case via spec
Defines defect skein modules for 3-manifolds with line and point defects and proves they match state spaces of defect Reshetikhin-Turaev TQFT for semisimple data.
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
Introduces the twisted Villain model to realize exact T-duality on the lattice for fibred manifolds, recovering bundle-flux exchange and defining topological defects via half-gauging.
Constructs a family of non-invertible topological defects in n Weyl fermion theories via unfolding of G-symmetric boundary conditions for Dirac fermions, with explicit descriptions for U(1)^n and applications to fermion-boundary scattering.
Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
Derives Schwinger-Dyson equations and Ward identities in NN-FT to study anomalies in QFTs via a conserved parameter-space current, yielding a new perspective on symmetries.
CMB polarization rotation emerges as a Pancharatnam phase localized at dark sector vacuum interfaces, independent of redshift, frequency, and the presence of light axions.
Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
A supersymmetric SymTFT (SuSymTFT) is constructed as a super-BF theory on (n|m)-dimensional supermanifolds and verified for compact and chiral super-bosons in two dimensions.
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Classification of 2D fermionic systems with Z2 flavor symmetry yields 16 consistent superfusion categories labeled by anomaly invariants (ν_W, ν_Z, ν_WZ).
A general prescription is formulated for spurion analysis of commutative non-invertible fusion algebras in particle physics, unifying prior specific cases and enabling systematic tracking of coupling constants in tree- and loop-level processes without requiring faithful realization or exclusive use.
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
A gauging method from abelian Dijkgraaf-Witten theories yields BF-type Lagrangians for non-abelian cases via local-coefficient cohomologies and homotopy analysis.
Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
citing papers explorer
-
CMB Birefringence from Vacuum Interfaces
CMB polarization rotation emerges as a Pancharatnam phase localized at dark sector vacuum interfaces, independent of redshift, frequency, and the presence of light axions.
-
de Sitter Vacua & pUniverses
The p-Schwinger model on de Sitter space supports p distinct de Sitter-invariant vacua that are Hadamard, and coupling a multi-flavor version to gravity yields a semiclassical de Sitter saddle at large N_f.
-
Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.