Abstract
Based on the rigorous path integral formulation of Liouville Conformal Field Theory initiated by David-Kupiainen-Rhodes-Vargas [6] on the Riemann sphere and David-Rhodes-Vargas [11] on the torus of modulus $\tau $, we give the exact asymptotic behaviour of the 1-point toric correlation function as $\mathrm{Im} \tau \to \infty $.
In agreement with formulae predicted within the bootstrap formalism of theoretical physics, our results feature an $(\mathrm{Im} \tau )^{-3/2}$ decay rate and we identify the derivative of DOZZ formula in the limit.
Citation
Guillaume Baverez. "Modular bootstrap agrees with the path integral in the large moduli limit." Electron. J. Probab. 24 1 - 22, 2019. https://doi.org/10.1214/19-EJP394
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