1993/08/26 by Leon A. Takhtajan, Leon Takhtajan · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Central charge #Conformal anomaly #Conformal field theory #Conformal map #Dimension (graph theory) #Liouville field theory #Mathematical analysis #Mathematical physics #Mathematics #Perturbation theory (quantum mechanics) #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Quantum, superfluid, helium dynamics #Relationship between string theory and quantum field theory #Riemann surface #Stochastic processes and statistical mechanics #String theory #hep-th
paper · pdf · doi:10.1142/s0217732393002269
published as Mod.Phys.Lett. A8 (1993) 3529-3536 · 8 pages, plain LaTex, submitted Mod. Phys. Lett. A
arxiv created 1993/08/26 · openalex publication_date 1993/12/07 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Inspired by Polyakov’s original formulation 1,2 of quantum Liouville theory through functional integral, we analyze perturbation expansion around a classical solution. We show the validity of conformal Ward identities for puncture operators and prove that their conformal dimension is given by the classical expression. We also prove that the total quantum correction to the central charge of Liouville theory is given by one-loop contribution, which is equal to 1. Applied to the bosonic string, this result ensures the vanishing of total conformal anomaly along the lines different from those presented by KPZ 3 and Distler-Kawai. 4