1307.0306 (Pietro Menotti)

Hyperbolic deformation of the strip-equation and the accessory
parameters for the torus    [PDF]

Pietro Menotti

By applying an hyperbolic deformation to the uniformization problem for the infinite strip, we give a method for computing the accessory parameter for the torus with one source as an expansion in the modular parameter q. At O(q^0) we obtain the same equation for the accessory parameter and the same value of the semiclassical action as the one obtained from the b -> 0 limit of the quantum one point function. The procedure can be carried over to the full O(q^2) or even higher order corrections although the procedure becomes somewhat complicated. Here we compute to order q^2 the correction to the weight parameter intervening in the conformal factor and it is shown that the unwanted contribution O(q) to the accessory parameter equation cancel exactly.

View original: http://arxiv.org/abs/1307.0306