Pith. sign in

REVIEW 4 cited by

4-Dimensional BF Theory as a Topological Quantum Field Theory

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 q-alg/9507006 v1 pith:FU36EJBC submitted 1995-07-10 q-alg gr-qchep-thmath.QA

classification q-alggr-qchep-thmath.QA
keywords equippedtheorycasedimensionalg-bundlemanifoldmanifoldsprincipal
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that 4-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G = GL(4,R) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of 4-manifolds.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. A 3BF model of quantum gravity coupled to Standard Model matter

    hep-th 2026-02 conditional novelty 6.0 of 10

    A 3BF higher-gauge model of quantum gravity with the full Standard Model is discretized on a piecewise-flat manifold, yielding a concrete path integral.

  2. Generalized forms of types N = 1, 2 and higher gauge theory

    math-ph 2026-01 conditional novelty 6.0 of 10

    Strict 2- and 3-gauge theory is re-expressed in a single generalized-form formalism in which higher connections, curvatures, Bianchi identities, and gauge transformations match ordinary gauge-theory form, yielding uni...

  3. The 3BF theory as a TQFT

    hep-th 2024-12 conditional novelty 6.0 of 10

    A boundary state sum for the 3BF theory is constructed and proved to satisfy Atiyah's axioms, giving a TQFT functor for finite 3-groups on triangulable 4-manifolds.

  4. Categorical quantum symmetries and ribbon tensor 2-categories

    math-ph 2025-01 reject novelty 5.0 of 10

    The paper constructs ribbon balancing data and framing levels for 2Rep(U_q G), making it a candidate ribbon tensor 2-category, and recovers strict pivotality in the classical limit q=1.

Pith tools