REVIEW 6 cited by
Isomonodromic tau-functions from Liouville conformal blocks
Not yet reviewed by Pith; the record is open.
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
abstract
The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with $SL(2,\mathbb{C})$-valued monodromy on Riemann surfaces of genus zero with $n$ punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at $c=1$. This implies a similar representation for the isomonodromic tau-function. In the case $n=4$ we thereby get a proof of the relation between tau-functions and conformal blocks discovered in \cite{GIL}. We briefly discuss a possible application of our results to the study of relations between certain $\mathcal{N}=2$ supersymmetric gauge theories and conformal field theory.
Forward citations
Cited by 6 Pith papers
-
On the Virasoro Crossing Kernels at Rational Central Charge
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.
-
Projecting Gravitational Fluctuations onto Near-Horizon Throats
A pair of coordinate changes projects Heun-type gravitational fluctuation equations onto two matched hypergeometric problems, reproducing instanton-counting results and yielding Schwarzian zero modes.
-
Blowing-up the edge: connection formulae and stability chart of the Lam\'e equation
The paper derives the resummed Nekrasov-Shatashvili free energy from blow-up equations and uses it to compute the band-gap structure, connection formulas, and stability chart of the Lamé equation.
-
Many-faced Painlev\'e I: irregular conformal blocks, topological recursion, and holomorphic anomaly approaches
The paper proves the conifold gap property for Weierstrass elliptic topological recursion and gives an algebraic construction of the rank 5/2 Virasoro Whittaker state, linking the Painlevé I tau function to CFT and ho...
-
(1,k) CFT and RH problem with the c=-2 case
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.
-
Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations
Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
Discussion (0). Sign in to comment.