Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions

Abstract

We present an approach that gives rigorous construction of a class of crossing invariant functions in $c=1$ CFTs from the weakly invariant distributions on the moduli space ${\mathcal{M}}_{0,4}^{SL(2,\mathbb{C})}$ of $SL(2,\mathbb{C})$ flat connections on the sphere with four punctures. By using this approach we show how to obtain correlation functions in the Ashkin-Teller and the Runkel-Watts theory. Among the possible crossing-invariant theories, we obtain also the analytic Liouville theory, whose consistence was assumed only on the basis of numerical tests.

arXiv comment39 pages, 4 figures, version in JHEP, fixed proof in sec. 6.4, updates in sec. 4.5, 4.6

References in corpus (24)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Two and three-point functions in Liouville theory
• Liouville theory revisited
• On the Liouville three-point function
• Darboux coordinates, Yang-Yang functional, and gauge theory
• Rolling Tachyons from Liouville theory
• A lecture on the Liouville vertex operators
• Renormalisation group calculation of correlation functions for the 2D random bond Ising and Potts models
• Liouville theory with a central charge less than one
• Isomonodromic tau-functions from Liouville conformal blocks
• A non-rational CFT with c=1 as a limit of minimal models
• A conformal bootstrap approach to critical percolation in two dimensions
• Three-point functions in c <= 1 Liouville theory and conformal loop ensembles
• Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator
• Monodromy dependence and connection formulae for isomonodromic tau functions
• Painlevé VI connection problem and monodromy of c=1 conformal blocks
• Potts q-color field theory and scaling random cluster model
• Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
• The analytic bootstrap equations of non-diagonal two-dimensional CFT
• Isomonodromic $\tau$-functions and $W_N$ conformal blocks
• Liouville field theory and log-correlated Random Energy Models
• Boundary conditions in Toda theories and minimal models
• Rigid Fuchsian systems in 2-dimensional conformal field theories

Cited by in corpus (3)

• Quantum spectral problems and isomonodromic deformations
• On the Virasoro fusion kernel at $c=25$
• Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model