Central charges without finite-size effects

Abstract

We show how to obtain the ultraviolet central charge from the exact S-matrix for a wide variety of models with a $U(1)$ symmetry. This is done by coupling the $U(1)$ current $J$ to a background field. In an $N$=2 superconformal theory with $J$ the fermion number current, the OPE of $J$ with itself and hence the free energy are proportional to $c$. By deforming the supersymmetry into affine $\hat{S}U(2{)}_q$ quantum-group symmetry, this result can be generalized to many $U(1)$-invariant theories, including the N=0 and N=1 sine-Gordon models and the $SU(2{)}_k$ WZW models. This provides a consistency check on a conjectured S-matrix completely independent of the finite-size effects expressed in terms of dilogarithms resulting from the thermodynamic Bethe ansatz.

11 pages, RU-93-26, BUHEP-93-16

References in corpus (5)

• Scattering and Thermodynamics of Fractionally-Charged Supersymmetric Solitons
• Scattering and Thermodynamics of Integrable N=2 Theories
• N=2 Supersymmetry, Painleve III and Exact Scaling Functions in 2D Polymers
• S-matrices for Perturbed N=2 Superconformal Field Theory from quantum groups
• S-matrix of N=2 Supersymmetric Sine-Gordon Theory

Cited by in corpus (5)

• Exact Conductance through Point Contacts in the $\nu =1/3$ Fractional Quantum Hall Effect
• Non-equilibrium DC noise in a Luttinger liquid with impurity
• Integrable theories that are asymptotically CFT
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• Thermodynamical Bethe Ansatz analysis in an SU(2)xU(1) symmetric sigma-model