The universal coefficient of the exact correlator of a large-$N$ matrix field theory

Abstract

Exact expressions have been proposed for correlation functions of the large-$N$ (planar) limit of the $(1+1)$-dimensional $\mathrm{SU}(N)\times \mathrm{SU}(N)$ principal chiral sigma model. These were obtained with the form-factor bootstrap. The short-distance form of the two-point function of the scaling field $\Phi (x)$, was found to be $N^{-1}⟨\mathrm{Tr}\Phi (0{)}^{†}\Phi (x)⟩=C_2{\ln }^{2}mx$, where $m$ is the mass gap, in agreement with the perturbative renormalization group. Here we point out that the universal coefficient $C_2$, is proportional to the mean first-passage time of a Lévy flight in one dimension. This observation enables us to calculate $C_2=1/16\pi$.

arXiv commentText lengthened from 3 to 6 pages, to include discussion of previous results and directions for further work. Some references added. Accepted for publication in Phys. Rev. D

References in corpus (14)

• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries
• Renormalization group flow with unstable particles
• Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function
• Multiparticle Form Factors of the Principal Chiral Model At Large N
• Summing Planar Diagrams by an Integrable Bootstrap II
• Summing Planar Diagrams by an Integrable Bootstrap
• The Spectrum of the Fractional Laplacian and First Passage Time Statistics
• Correlation Functions of the SU(infinity) Principal Chiral Model
• Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
• Seeing asymptotic freedom in an exact correlator of a large-$N$ matrix field theory
• (2+1)-Dimensional Yang-Mills Theory and Form Factor Perturbation Theory
• Nontrivial Thermodynamics in 't Hooft's Large-$N$ Limit
• The spectrum of large powers of the Laplacian in bounded domains

Cited by in corpus (1)

• The two-dimensional twisted reduced principal chiral model revisited