Pith Number

pith:JEKMBEMZ

pith:2026:JEKMBEMZHDKHFW5PWRDWLXSXHW

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$c=1$ strings as a matrix integral

Lorenz Eberhardt, Scott Collier, Victor A. Rodriguez

The c=1 string's perturbative S-matrix is equivalently described by a double-scaled matrix integral with spectral curve x(z)=2√2 cos(z), y(z)=sin(z).

arxiv:2604.06301 v2 · 2026-04-07 · hep-th

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Claims

C1strongest claim

We study the perturbative S-matrix of the c=1 string and show that it admits a description in terms of a double-scaled (0+0)-dimensional matrix integral based on the spectral curve x(z) = 2√2 cos(z), y(z)=sin(z). Combined with the famous duality to matrix quantum mechanics, this establishes a triality between three formulations of the theory: the worldsheet description, matrix quantum mechanics, and a matrix integral.

C2weakest assumption

The physical S-matrix elements are recovered by restriction to the first Brillouin zone followed by analytic continuation to Lorentzian kinematics from the intersection-number expressions that describe a discretized target space.

C3one line summary

The c=1 string perturbative S-matrix equals a double-scaled (0+0)-dimensional matrix integral on the spectral curve x(z)=2√2 cos(z), y(z)=sin(z), establishing triality with worldsheet and matrix quantum mechanics descriptions.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

The Super Virasoro Minimal String from 3d Supergravity

Receipt and verification

First computed	2026-05-27T02:05:19.214364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4914c0919938d472dbafb44765de573d94952604af6956f7dda8821015fd58b0

Aliases

arxiv: 2604.06301 · arxiv_version: 2604.06301v2 · doi: 10.48550/arxiv.2604.06301 · pith_short_12: JEKMBEMZHDKH · pith_short_16: JEKMBEMZHDKHFW5P · pith_short_8: JEKMBEMZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JEKMBEMZHDKHFW5PWRDWLXSXHW \
  | 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: 4914c0919938d472dbafb44765de573d94952604af6956f7dda8821015fd58b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab9bf9f9bb1b782d0ac7f6e2dd0e930b462acf9615b0970a815f174aa06bd857",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-04-07T18:00:00Z",
    "title_canon_sha256": "e3f8ecf0bed9d65c6d67cec18271a250bf1bad93ea4c7b786479cfed9642ace5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06301",
    "kind": "arxiv",
    "version": 2
  }
}