On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

Details On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

2010-03-29

arxiv.org/abs/1003.5542v3

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, 2 figures, v2: minor corrections, v3: minor corrections and references added

Scientific paper

We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if both the density of states in rapidity space and the quadratic fluctuations around the saddle point solution to the TBA are properly taken into account. In relativistic boundary QFT the O(1) contributions are directly related to the exact g-function. In this paper we provide an all-orders proof of the previous results of P. Dorey et al. on the g-function in both massive and massless models. In addition, we derive a new result for the g-function which applies to massless theories with arbitrary diagonal scattering in the bulk.

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