Modular bootstrap agrees with path integral in the large moduli limit

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 $\tau$, 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.

arXiv comment24 pages, 3 figures

References in corpus (14)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• Analytic Continuation of Liouville Theory
• On the Liouville three-point function
• Liouville Quantum Gravity on the complex tori
• Conformal field theory on the plane
• Modular bootstrap in Liouville field theory
• Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity
• Gaussian multiplicative chaos and applications: a review
• The DOZZ Formula from the Path Integral
• Minisuperspace limit of the AdS3 WZNW model
• Renormalizability of Liouville Quantum Gravity at the Seiberg bound
• The distribution of Gaussian multiplicative chaos on the unit interval
• Exercices sur les temps locaux de semi-martingales continues et les excursions browniennes

Cited by in corpus (3)

• Fusion asymptotics for Liouville correlation functions
• Probabilistic conformal blocks for Liouville CFT on the torus
• Path integral approach to analytic continuation of Liouville theory: the pencil region