Pith. sign in

REVIEW 5 cited by

Global Anomalies on the Hilbert Space

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

arxiv 2101.02218 v3 pith:J6KYSGZ5 submitted 2021-01-06 hep-th cond-mat.str-el

Global Anomalies on the Hilbert Space

classification hep-th cond-mat.str-el
keywords hilbertanomaliesanomalousspacetqftsdimensionsdistinctglobal
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology "layers" that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2+1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Anomaly-induced vanishing of brane partition functions

    hep-th 2025-10 conditional novelty 6.0

    Anomalies imply vanishing brane partition functions; this yields unified derivations of the Freed-Witten and M5 shifted-quantization conditions and new S-fold D3-brane constraints.

  2. Tori, Klein Bottles, and Modulo 8 Parity/Time-reversal Anomalies of 2+1d Staggered Fermions

    hep-th 2026-01 unverdicted novelty 5.0

    Staggered fermions in 2+1d show modulo 8 parity/time-reversal anomalies that match between lattice and continuum when placed on tori and Klein bottles via a nontrivial symmetry map.

  3. Global symmetries: locality, unitarity, and regularity

    hep-th 2025-11 unverdicted novelty 5.0

    Authors introduce an observable measuring non-locality properties of symmetry operators that encodes fusion algebra information for a class of examples in QFT.

  4. What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries

    hep-th 2023-08 unverdicted novelty 3.0

    A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.

  5. Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

    hep-th 2022-05 unverdicted novelty 2.0

    This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.