On the monodromy problem for the four-punctured sphere

DOI10.1088/1751-8113/47/41/415201zbMATH Open1302.33014arXiv1401.2409OpenAlexW2018889322MaRDI QIDQ2927694

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Publication date: 4 November 2014

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Abstract: We consider the monodromy problem for the four-punctured 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 infinite central charge. The integrals which 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.

Full work available at URL: https://arxiv.org/abs/1401.2409

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