Pith. sign in

REVIEW 5 cited by

Anomalies and Bounds on Charged Operators

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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 1904.04833 v3 pith:CTQFDTW7 submitted 2019-04-09 hep-th cond-mat.str-el

Ying-Hsuan Lin , Shu-Heng Shao This is my paper · ORCID
classification hep-thcond-mat.str-el
keywords symmetrymathbbboundboundsgloballightestnon-anomalousthere
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We study the implications of 't Hooft anomaly (i.e. obstruction to gauging) on conformal field theory, focusing on the case when the global symmetry is $\mathbb{Z_2}$. Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal $\mathbb{Z_2}$ global symmetry are derived. The bootstrap bounds depend dramatically on the 't Hooft anomaly. In particular, there is a universal upper bound on the lightest $\mathbb{Z_2}$ odd operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous. In the non-anomalous case, we find that the lightest $\mathbb{Z_2}$ odd state and the defect ground state cannot both be arbitrarily heavy. We also consider theories with a $U(1)$ global symmetry, and comment that there is no bound on the lightest $U(1)$ charged operator if the symmetry is non-anomalous.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

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

  1. Disjoint additivity and local quantum physics

    hep-th 2025-09 conditional novelty 7.0 of 10

    Local quantum systems should obey disjoint additivity plus Haag duality, a combination that survives higher-form symmetries and fails for known nonlocal constructions.

  2. Non-Local Conserved Currents and Continuous Non-Invertible Symmetries

    hep-th 2025-07 conditional novelty 7.0 of 10

    Non-local conserved currents attached to topological lines generate continuous non-invertible symmetries in 1+1d CFTs, with new examples in SU(2)_k WZW and minimal model products.

  3. Coupled minimal models revisited II: Constraints from permutation symmetry

    hep-th 2024-12 accept novelty 7.0 of 10

    For coupled large-m minimal models with N=5,6,7, every permutation-charged current below spin 10 acquires an anomalous dimension, so the IR fixed points show no extended chiral algebra in that range.

  4. Topological Transition on the Conformal Manifold

    cond-mat.str-el 2019-09 conditional novelty 7.0 of 10

    Fermionic conformal field theories on a line of couplings can pair up so that opposite sides differ by an invertible topological order, a continuous topological transition that maps to Kramers-Wannier duality after bo...

  5. Two-dimensional Anomaly, Orbifolding, and Boundary States

    hep-th 2019-08 conditional novelty 6.0 of 10

    A modular S-transformation criterion on twisted torus partition functions detects zero-form discrete symmetry anomalies in 2D RCFTs, and it matches boundary-state and orbifold conditions in WZW models.

Pith tools