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

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Pisa, and INFN — Sezione di Pisa, Largo B. Pontecorvo 3, I-56127, Pisa, Italy

    Pietro Menotti

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  1. Pietro Menotti
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Correspondence to Pietro Menotti.

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ArXiv ePrint: 1307.0306

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Menotti, P. Hyperbolic deformation of the strip-equation and the accessory parameters for the torus. J. High Energ. Phys. 2013, 132 (2013). https://doi.org/10.1007/JHEP09(2013)132

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  • DOI: https://doi.org/10.1007/JHEP09(2013)132

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