The Coleman correspondence at the free fermion point

Abstract

We prove that the truncated correlation functions of the charge and gradient fields associated with the massless sine-Gordon model on ${\mathbb{R}}^2$ with $\beta =4\pi$ exist for all coupling constants and are equal to those of the chiral densities and vector current of free massive Dirac fermions. This is an instance of Coleman's prediction that the massless sine-Gordon model and the massive Thirring model are equivalent (in the above sense of correlation functions). Our main novelty is that we prove this correspondence starting from the Euclidean path integral in the non-perturative regime of the infinite volume models. We use this correspondence to show that the correlation functions of the massless sine-Gordon model with $\beta =4\pi$ decay exponentially and that the corresponding probabilistic field is localized.

arXiv commentInsignificant sign error corrected

References in corpus (11)

• Exact expectation values of local fields in quantum sine-Gordon model
• Non linear integral equation and excited--states scaling functions in the sine-Gordon model
• Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point
• Functional Integral Construction of the Thirring model: axioms verification and massless limit
• Height fluctuations in interacting dimers
• Sine-Gordon Revisited
• Massless Sine-Gordon and Massive Thirring Models: proof of the Coleman's equivalence
• Log-Sobolev inequality for the continuum sine-Gordon model
• A probabilistic approach of ultraviolet renormalisation in the boundary Sine-Gordon model
• Maximum and coupling of the sine-Gordon field
• Conformal bootstrap in Liouville Theory

Cited by in corpus (7)

• Stochastic dynamics and the Polchinski equation: an introduction
• Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces
• Conformal invariance and Renormalization Group
• The Sine-Gordon QFT in de Sitter spacetime
• Conformal field theory, solitons, and elliptic Calogero--Sutherland models
• On the duality between height functions and continuous spin models
• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor