Matching branches of a~nonperturbative conformal block at its singularity divisor
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 3-40
Voir la notice de l'article provenant de la source Math-Net.Ru
A conformal block is a function of many variables, usually represented as a formal series with coefficients that are certain matrix elements in the chiral {(}i.e., Virasoro{\rm)} algebra. A nonperturbative conformal block is a multivalued function defined globally over the space of dimensions and has many branches and, perhaps, additional free parameters not seen at the perturbative level. We discuss additional complications of the nonperturbative description that arise because all the best-studied examples of conformal blocks are at the singularity locus in the moduli space {\rm(}at divisors of the coefficients or, simply, at zeros of the Kac determinant{\rm).} A typical example is the Ashkin–Teller point, where at least two naive nonperturbative expressions are provided by the elliptic Dotsenko–Fateev integral and by the celebrated Zamolodchikov formula in terms of theta constants, and they differ. The situation is somewhat similar at the Ising and other minimal model points.
Keywords:
two-dimensional conformal theory, conformal block.
@article{TMF_2015_184_1_a0,
author = {H. Itoyama and A. D. Mironov and A. Yu. Morozov},
title = {Matching branches of a~nonperturbative conformal block at its singularity divisor},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {3--40},
publisher = {mathdoc},
volume = {184},
number = {1},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a0/}
}
TY - JOUR AU - H. Itoyama AU - A. D. Mironov AU - A. Yu. Morozov TI - Matching branches of a~nonperturbative conformal block at its singularity divisor JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2015 SP - 3 EP - 40 VL - 184 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a0/ LA - ru ID - TMF_2015_184_1_a0 ER -
%0 Journal Article %A H. Itoyama %A A. D. Mironov %A A. Yu. Morozov %T Matching branches of a~nonperturbative conformal block at its singularity divisor %J Teoretičeskaâ i matematičeskaâ fizika %D 2015 %P 3-40 %V 184 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a0/ %G ru %F TMF_2015_184_1_a0
H. Itoyama; A. D. Mironov; A. Yu. Morozov. Matching branches of a~nonperturbative conformal block at its singularity divisor. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 3-40. http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a0/