Pith. sign in

REVIEW 3 cited by

Painlev\'e VI connection problem and monodromy of c=1 conformal blocks

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1308.4092 v2 pith:EXASCFSR submitted 2013-08-19 hep-th math-phmath.MP

N. Iorgov , O. Lisovyy , Yu. Tykhyy This is my paper
classification hep-thmath-phmath.MP
keywords conformalfunctionblocksconnectionintegrationmonodromypainlevarguments
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

Generic c=1 four-point conformal blocks on the Riemann sphere can be seen as the coefficients of Fourier expansion of the tau function of Painlev\'e VI equation with respect to one of its integration constants. Based on this relation, we show that c=1 fusion matrix essentially coincides with the connection coefficient relating tau function asymptotics at different critical points. Explicit formulas for both quantities are obtained by solving certain functional relations which follow from the tau function expansions. The final result does not involve integration and is given by a ratio of two products of Barnes G-functions with arguments expressed in terms of conformal dimensions/monodromy data. It turns out to be closely related to the volume of hyperbolic tetrahedron.

Discussion (0). Sign in to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Virasoro Crossing Kernels at Rational Central Charge

    hep-th 2025-12 conditional novelty 8.0 of 10

    At rational central charge, the Virasoro crossing kernels decompose into two admissible square-root-branched kernels; the physical c≤1 kernels are derived for the first time.

  2. Modular transformations of tau functions and conformal blocks on the torus

    math-ph 2025-08 conditional novelty 8.0 of 10

    The paper derives the modular connection constant for tau functions on the one-punctured torus and obtains an exact closed formula for the c=1 Virasoro modular kernel.

  3. (1,k) CFT and RH problem with the c=-2 case

    math-ph 2026-07 conditional novelty 6.0 of 10

    For (1,k) Virasoro models, periodic vertex operators plus two degenerate fields solve a modified Riemann–Hilbert problem; in the k=2, c=-2 case the solution is explicit and satisfies new bilinear identities.

Pith tools