Reflection factors for the principal chiral model

Andrei I. Maimistov

Anastasia Doikou, Andrei Babichenko

We consider the SU(2) Principal Chiral Model (at level k = 1) on the half-line with scale invariant boundary conditions. By looking at the IR limiting conformal field theory and comparing with the Kondo problem, we propose the set of The principal chiral model PCMk is defined by the action:

J. N. Prata, Grupo De Astrofísica E Cosmologia

We compute the boundary entropies for the allowed boundary conditions of the SU(2)-invariant principal chiral model at level k=1. We used the reflection factors determined in ref.\\cite{27}. As a by-product we obtain some miscellaneous results such as the ground-state energy for mixed boundary conditions as well as the degeneracies of the Kondo model in the underscreened and exactly screened cases. All these computations are in perfect agreement with known results.

R. J. Baxter

We derive the free energy of the chiral Potts model by the infinite lattice “inversion relation” method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice functional relations, we find that in addition to the usual assumption that the free energy be analytic and bounded in some principal domain of the rapidity parameter space that includes the physical regime, we also need a much less obvious symmetry. We can then obtain the free energy by Wiener-Hopf ~factorization in the complex planes of appropriate variables. Together with the inversion relation, this symmetry relates the values of the free energy in all neighbouring domains to those in the principal domain.

V. F. M�ller