The exact mass-gaps of the principal chiral models

T.J. Hollowood

The exact mass-gaps of the principal chiral models

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arxiv hep-th/9402084 v1 pith:Z4VN7SS4 submitted 1994-02-15 hep-th

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keywords exactcalculationchiralmatrixmodelsprincipalscatteringtheory

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abstract

An exact expression for the mass-gap, the ratio of the physical particle mass to the $\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.

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A unified Wiener-Hopf construction gives all-order trans-series for conserved charges in O(N), SU(N), Lieb-Liniger, Gaudin-Yang and capacitor models, with numerically checked Borel resummation.

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