Pith Number

pith:OIAMTXF3

pith:2025:OIAMTXF3XQWPDGL3R7YHU4GUPR

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2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging

Benjamin Haake, Nils Carqueville

Gauging the 0-form G-symmetry on the neutral component of a G-crossed braided fusion category produces its equivariantisation, which has a generalised symmetry that gauges back to the original.

arxiv:2506.08178 v1 · 2025-06-09 · math.QA · hep-th · math-ph · math.MP

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Claims

C1strongest claim

In the special case of Reshetikhin-Turaev theories coming from G-crossed braided fusion categories C^×_G, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form G-symmetry on the neutral component C_e of C^×_G produces its equivariantisation (C^×_G)^G, which in turn features a generalised symmetry whose gauging recovers C_e.

C2weakest assumption

These symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data.

C3one line summary

The paper proves that 2-group symmetries in 3D defect TQFTs from G-crossed braided fusion categories have no gauging obstructions and that gauging the 0-form G-symmetry on the neutral component produces the equivariantisation, with a reciprocal relation when G is commutative.

References

14 extracted · 14 resolved · 4 Pith anchors

[1] Butterflies I: morphisms of 2-group stacks 2009 · doi:10.1016/j.aim

[2] Lecture notes on two-dimensional defect TQFT , volume= 2024 · doi:10.4064/bc114-2

[3] Orbifold completion of 3-categories 2023

[4] The 1{Nexpansion of the symmetric traceless and the antisymmetric tensor models in rank three 2016 · doi:10.1007/s00220-

[5] Orbifolds of n-dimensional defect TQFTs 2019 · arXiv:1705.06085

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T01:04:55.009934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7200c9dcbbbc2cf1997b8ff07a70d47c68d1b7f8baf8db935df26c88a1582fd7

Aliases

arxiv: 2506.08178 · arxiv_version: 2506.08178v1 · doi: 10.48550/arxiv.2506.08178 · pith_short_12: OIAMTXF3XQWP · pith_short_16: OIAMTXF3XQWPDGL3 · pith_short_8: OIAMTXF3

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OIAMTXF3XQWPDGL3R7YHU4GUPR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7200c9dcbbbc2cf1997b8ff07a70d47c68d1b7f8baf8db935df26c88a1582fd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa2c2fb5b1223b4bcfee38acd9096e20bda5aa5f5b9806fb446c8239d078918f",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2025-06-09T19:42:49Z",
    "title_canon_sha256": "676a4b945b30b70334289df393f54f467897743d8217b097cd8f881b7277c6ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08178",
    "kind": "arxiv",
    "version": 1
  }
}