Pith Number

pith:CSGNYT4A

pith:2024:CSGNYT4AY2F4N34QX65YZTL2W6

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Left-Right Relative Entropy

Mostafa Ghasemi

Left-right relative entropy vanishes between certain orthogonal boundary states in 2D CFTs, defining new equivalence classes called relative entanglement sectors.

arxiv:2411.09406 v4 · 2024-11-14 · hep-th · math-ph · math.MP · quant-ph

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Claims

C1strongest claim

the left-right relative entropy between certain reduced boundary states vanishes even though the corresponding global boundary states are orthogonal. This observation motivates the introduction of relative entanglement sectors, defined as equivalence classes of boundary states that are indistinguishable with respect to left-right relative entropy. These sectors transform as NIM-representations of global symmetries and exhibit level-dependent structures that mirror Z2 't Hooft anomalies.

C2weakest assumption

The assumption that tracing over left- or right-moving modes of regularized boundary states on a circle produces a valid probability distribution determined entirely by the modular S-matrix and boundary data, allowing the quantity to be interpreted as a Kullback-Leibler divergence (abstract, paragraph on derivation of universal formula).

C3one line summary

Introduces left-right relative entropy for 2d CFT boundary states that reduces to KL divergence via modular data, revealing relative entanglement sectors linked to 't Hooft anomalies in models like Ising and WZW.

Cited by

1 paper in Pith

Defect relative entropy in symmetric orbifold CFTs

Receipt and verification

First computed	2026-05-26T02:03:47.153611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

148cdc4f80c68bc6ef90bfbb8ccd7ab7a4d1d942c0b0b0c5edaa05620add0f58

Aliases

arxiv: 2411.09406 · arxiv_version: 2411.09406v4 · doi: 10.48550/arxiv.2411.09406 · pith_short_12: CSGNYT4AY2F4 · pith_short_16: CSGNYT4AY2F4N34Q · pith_short_8: CSGNYT4A

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CSGNYT4AY2F4N34QX65YZTL2W6 \
  | 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: 148cdc4f80c68bc6ef90bfbb8ccd7ab7a4d1d942c0b0b0c5edaa05620add0f58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c07b4fba2690f961ad41338422e89c6614e0014e8517cd823f373e611ec1a6e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2024-11-14T12:45:59Z",
    "title_canon_sha256": "e636ec5ff9e1428e65b8441db2a73380a58c2fa1b2eda9460d6114891e480017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.09406",
    "kind": "arxiv",
    "version": 4
  }
}