Integrable theories that are asymptotically CFT
Jul, 199423 pages
Published in:
- Nucl.Phys.B 438 (1995) 469-490
e-Print:
- hep-th/9407113 [hep-th]
Report number:
- CERN-TH-7293-94,
- SWAT-93-94-32
Citations per year
Abstract:
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level . In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-function and allows for an evaluation of the mass gap (the ratio of the physical mass to the -parameter) to leading order in .- sigma model: nonlinear
- field theory: action
- dimension: 2
- torsion
- current algebra
- perturbation theory: higher-order
- renormalization
- energy
- integrability
- asymptotic behavior
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