Central charges without finite-size effects

Details Central charges without finite-size effects Central charges without finite-size effects

1993-07-15

arxiv.org/abs/hep-th/9307101v1

Phys.Lett. B319 (1993) 132-138

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0370-2693(93)90792-G

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 $\widehat SU(2)_q$ 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.

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