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pith:OWYAY52X

pith:2023:OWYAY52XYP5ZLZN2FOSR5NIW7Q

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ICTP Lectures on (Non-)Invertible Generalized Symmetries

Sakura Schafer-Nameki

Non-invertible symmetries arise when a quantum field theory is stacked with topological QFTs and a diagonal symmetry is gauged, producing topological defects without inverses.

arxiv:2305.18296 v2 · 2023-05-29 · hep-th · cond-mat.str-el · hep-ph · math.CT

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Claims

C1strongest claim

The main idea that underlies many constructions of non-invertible symmetries is that of stacking a QFT with topological QFTs (TQFTs) and then gauging a diagonal non-anomalous global symmetry. The TQFTs become topological defects in the gauged theory called (twisted) theta defects.

C2weakest assumption

The foundational identification of symmetries with topological defects in a general QFT holds and extends consistently to the non-invertible case via the stacking-and-gauging construction.

C3one line summary

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.

References

161 extracted · 161 resolved · 23 Pith anchors

[1] Generalized Global Symmetries 2015 · arXiv:1412.5148

[2] 205, American Mathematical Society, Providence, RI, 2015,MR3242743 DOI:10.1090/surv/205 2015 · doi:10.1090/surv/205

[3] Kramers-Wannier duality from conformal defects 2004 · arXiv:cond-mat/0404051

[4] Topological defects for the free boson CFT 2007 · arXiv:0705.3129

[5] Defect lines, dualities, and generalised orbifolds,

Cited by

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Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT

Receipt and verification

First computed	2026-05-17T23:38:48.610391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75b00c7757c3fb95e5ba2ba51eb516fc2d35d6fad78b41906395a61495e6d489

Aliases

arxiv: 2305.18296 · arxiv_version: 2305.18296v2 · doi: 10.48550/arxiv.2305.18296 · pith_short_12: OWYAY52XYP5Z · pith_short_16: OWYAY52XYP5ZLZN2 · pith_short_8: OWYAY52X

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OWYAY52XYP5ZLZN2FOSR5NIW7Q \
  | 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: 75b00c7757c3fb95e5ba2ba51eb516fc2d35d6fad78b41906395a61495e6d489

Canonical record JSON

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    "primary_cat": "hep-th",
    "submitted_at": "2023-05-29T17:59:50Z",
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