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arXiv · 1805.09766

Modular bootstrap agrees with path integral in the large moduli limit

Guillaume Baverez
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Abstract

Based on the rigorous path integral formulation of Liouville Conformal Field Theory initiated by David-Kupiainen-Rhodes-Vargas on the Riemann sphere and David-Rhodes-Vargas on the torus of modulus $τ$, we give the exact asymptotic behaviour of the 1-point toric correlation function as $\mathrm{Im}\:τ\to\infty$. In agreement with formulae predicted within the bootstrap formalism of theoretical physics, our results feature an $(\mathrm{Im}\:τ)^{-3/2}$ decay rate and we identify the derivative of DOZZ formula in the limit.

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Guillaume Baverez. 2019-12-06. Modular bootstrap agrees with path integral in the large moduli limit. https://doi.org/10.1214/19-ejp394

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