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Integrable theories that are asymptotically CFT
Nuclear Physics B, Volume: "B438", Issue: 3, Pages: 469 - 490
Swansea University Author:
Timothy Hollowood
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DOI (Published version): 10.1016/0550-3213(94)00473-R
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 $k$. In contrast to the more familiar situation of asymptotically free theories in which the fixe...
| Published in: | Nuclear Physics B |
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| ISSN: | 05503213 |
| Published: |
1994
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa28583 |
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| 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 $k$. 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 $\Lambda$-parameter) to leading order in |
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| College: |
Faculty of Science and Engineering |
| Issue: |
3 |
| Start Page: |
469 |
| End Page: |
490 |