Pith Number

pith:YWRJKAQQ

pith:2026:YWRJKAQQ33NMKJKVDTMYTKOGAV

not attested not anchored not stored refs pending

Quantum Flat Connections, KZ equations, and Integrability

Anouchah Latifi, Babak Haghighat, Sibasish Banerjee

Quantum flat connections in strongly coupled Argyres-Douglas theories are integrable and equivalent to irregular KZ connections that yield BPZ equations.

arxiv:2604.26159 v2 · 2026-04-28 · hep-th · math.RT

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\pithnumber{YWRJKAQQ33NMKJKVDTMYTKOGAV}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

we show that the corresponding flat bundle over C can be quantized such that the resulting quantum flat connection is integrable. For sl_2, the quantum connection takes values in gl_2(A) where A is an associative algebra which we explicitly describe for the cases of Painlevé I, II and IV. Moreover, we find that the quantum connection is equivalent to irregular versions of Knizhnik-Zamolodchikov (KZ) connections. Utilizing a suitable gauge transformation, one can show that the corresponding KZ equations give rise to BPZ equations.

C2weakest assumption

The standard Hitchin-system description of N=2 SYM theories (especially strongly coupled Argyres-Douglas points) admits a quantization that preserves integrability and produces an equivalence to irregular KZ connections.

C3one line summary

Quantum flat connections in strongly coupled Argyres-Douglas theories are integrable and equivalent to irregular KZ connections that yield BPZ equations.

Receipt and verification

First computed	2026-05-28T01:04:40.919481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5a2950210dedac525551cd989a9c6054bde49093e1a10800a45098e7f861e10

Aliases

arxiv: 2604.26159 · arxiv_version: 2604.26159v2 · doi: 10.48550/arxiv.2604.26159 · pith_short_12: YWRJKAQQ33NM · pith_short_16: YWRJKAQQ33NMKJKV · pith_short_8: YWRJKAQQ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YWRJKAQQ33NMKJKVDTMYTKOGAV \
  | 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: c5a2950210dedac525551cd989a9c6054bde49093e1a10800a45098e7f861e10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb9fafcacdc2b476bcf3de653e213a45f3ac120e2b9f8cf1d691607245533fb9",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-04-28T22:40:53Z",
    "title_canon_sha256": "5d0df47daf4271b9beeb5bb083b6ab79b04f511bffacca631ad3abfcd0b40019"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26159",
    "kind": "arxiv",
    "version": 2
  }
}