Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models

Abstract

We study Virasoro minimal-model 4-point conformal blocks on the sphere and 0-point conformal blocks on the torus (the Virasoro characters), as solutions of Zamolodchikov-type recursion relations. In particular, we study the singularities due to resonances of the dimensions of conformal fields in minimal-model representations, that appear in the intermediate steps of solving the recursion relations, but cancel in the final results.

arXiv comment26 pages, 1 figure minor modifications

References in corpus (9)

• Recursion relations in CFT and N=2 SYM theory
• On AGT conjecture
• Recursive representation of the torus 1-point conformal block
• Virasoro conformal blocks in closed form
• Liouville theory with a central charge less than one
• A conformal bootstrap approach to critical percolation in two dimensions
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions

Cited by in corpus (4)

• On 2d CFTs that interpolate between minimal models
• Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model