REVIEW 19 cited by
Condensations in higher categories
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Condensations in higher categories
read the original abstract
We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our construction replaces the idempotents in the ordinary version with a notion that we call "condensations." The name is justified by the direct physical interpretation of the notion of condensation: it encodes a general class of constructions which produce a new topological phase of matter by turning on a commuting projector Hamiltonian on a lattice of defects within a different topological phase, which may be the trivial phase. We also identify our higher Karoubi envelopes with categories of fully-dualizable objects. Together with the Cobordism Hypothesis, we argue that this realizes an equivalence between a very broad class of gapped topological phases of matter and fully extended topological field theories, in any number of dimensions.
Forward citations
Cited by 19 Pith papers
-
Pro-Tensor Network
Introduces pro-tensor networks as a categorified graphical framework for many-many-body theories, recovers the Levin-Wen model, characterizes particles as modules over promonads, and relaxes semisimplicity, finiteness...
-
Homotopy Posets, Postnikov Towers, and Hypercompletions of $\infty$-Categories
Homotopy posets assemble into an oriented long exact sequence analogue and form layers of a categorical Postnikov tower, with Postnikov-complete (∞,∞)-categories identified as the limit of (∞,n)-categories along trunc...
-
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.
-
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 latt...
-
Pro-Tensor Network
Pro-tensor networks form a categorified framework for many-many-body theories that recovers the Levin-Wen model and characterizes particles as modules over promonads without requiring semisimplicity, finiteness or rigidity.
-
Half-Spacetime Gauging of 2-Group Symmetry in 3d
Half-spacetime gauging of 2-group symmetries in (2+1)d QFTs produces non-invertible duality defects whose fusion rules are derived explicitly from parent theories with mixed anomalies.
-
Half-Spacetime Gauging of 2-Group Symmetry in 3d
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.
-
Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
-
The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise
Pauli stabilizer codes are classified via algebraic L-theory, yielding a bulk-boundary map to Clifford QCAs and a structural comparison with continuum framed TQFTs.
-
Generalized Complexity Distances and Non-Invertible Symmetries
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.
-
The Line, the Strip and the Duality Defect
Condensation defects in SymTFT descriptions of XY-plaquette and XYZ-cube models realize non-invertible self-duality symmetries at any coupling, with a continuous SO(2) version in the XY-plaquette.
-
Higher Gauging and Non-invertible Condensation Defects
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.
-
Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories
A coherent dual of an object lifts to a coherent dual of a bimodule over Frobenius algebras; zigzag 2-isos need special Frobenius sections, and special Frobenius algebras in 2Vect are rigid.
-
Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space fact...
-
Notes on (-2)-form symmetries
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...
-
Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories
Explicit construction of dual bimodules from Frobenius algebras in monoidal 2-categories, with promotion of coherent duals and proof that special Frobenius algebras in 2Vect are rigid.
-
What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
-
ICTP Lectures on (Non-)Invertible Generalized Symmetries
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
-
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.