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On the monodromy problem for the four-punctured sphere · Around

2014

On the monodromy problem for the four-punctured sphere

Menotti, Pietro

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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.

Built on

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Al.B. Zamolodchikov, Conformal Symmetry In Two-dimensions: An Explicit Recurrence Formula For The Conformal Partial Wave Amplitude
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Al.B. Zamolodchikov, Conformal symmetry in two-dimensions: recursion representation of conformal block
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A.B. Zamolodchikov, Al.B. Zamolodchikov, Conformal bootstrap in Liouville field theory
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