On the monodromy problem for the fourpunctured sphere
Abstract
We consider the monodromy problem for the fourpunctured sphere in which the character of one composite monodromy is fixed, by looking at the expansion of the accessory parameter in the modulus x directly, without taking the limit of the quantum conformal blocks for an infinite central charge. The integrals that appear in the expansion of the Volterra equation involve products of two hypergeometric functions to first order and up to four hypergeometric functions to second order. It is shown that all such integrals can be computed analytically. We give the complete analytical evaluation of the accessory parameter to first and second order in the modulus. The results agree with the evaluation obtained by assuming the exponentiation hypothesis of the quantum conformal blocks in the limit of infinite central charge. Extension to higher orders is discussed.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2014
 DOI:
 10.1088/17518113/47/41/415201
 arXiv:
 arXiv:1401.2409
 Bibcode:
 2014JPhA...47O5201M
 Keywords:

 High Energy Physics  Theory
 EPrint:
 14 pages LaTeX, 1 figure. Notation improved