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.
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Topological Defect Lines and Renormalization Group Flows in Two Dimensions
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We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.
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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.
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.
Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left-right symmetries and boundary conditions in 2D CFTs.
Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
RG domain walls between Z_N parafermions and minimal models support a continuous defect conformal manifold generated by a spin-1 phantom current, with transmission rate vanishing at large N.
A new TIM/Ising conformal interface is identified with emergent W3 symmetry, yielding defect spectrum predictions for Rydberg atom experiments.
Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.
Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
Constructs non-invertible duality defects in (2+1)d QFTs from half-spacetime gauging of 2-group symmetries and derives explicit fusion rules with examples in U(1)^3 gauge theories.
Tensor renormalization group computes symmetry-twisted partition functions to identify critical points solely from them, yielding Tc=2.2017(2) and nu=0.663(33) for the 3D O(2) model plus TBKT=0.8928(2) for the 2D O(2) BKT transition.
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
Constructs Symmetry TFTs for M-theory compactifications by reducing the topological sector of 11d supergravity on the boundary of X using differential cohomology, with applications to 7d SYM and 5d SCFTs confirmed via IIB 5-brane webs.
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.
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.
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 kink in a one-link mass term for 3+1D staggered fermions creates a 2+1D domain wall with two-flavor massless Dirac fermions protected by SU(2) and parity, realizing the parity anomaly from the UV lattice Hamiltonian.
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Entanglement-spectrum fingerprint of a non-invertible symmetry: the Kramers--Wannier duality defect on the lattice
The categorical data of the KW duality defect, including its quantum dimension sqrt(2), is encoded in the entanglement spectrum of the duality-twisted Ising ground state through a Majorana zero mode.