Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 7 (2011), 007, 36 pages      arXiv:1010.0858      http://dx.doi.org/10.3842/SIGMA.2011.007
Contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”

Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States

Hermann Boos a, b
a) Fachbereich C – Physik, Bergische Universität Wuppertal, 42097 Wuppertal, Germany
b) Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991 Moscow, Russia

Received October 07, 2010, in final form January 05, 2011; Published online January 13, 2011

Abstract
We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction. We establish an equivalence between a scaling limit of the partition function of the six-vertex model on a cylinder with quasi-local operators inserted and special boundary conditions, corresponding to particle-hole excitations, on the one hand, and certain three-point correlation functions of conformal field theory (CFT) on the other hand. As in hidden Grassmann structure IV, the fermionic basis developed in previous papers and its conformal limit are used for a description of the quasi-local operators. In paper IV we claimed that in the conformal limit the fermionic creation operators generate a basis equivalent to the basis of the descendant states in the conformal field theory modulo integrals of motion suggested by A. Zamolodchikov (1987). Here we argue that, in order to completely determine the transformation between the above fermionic basis and the basis of descendants in the CFT, we need to involve excitations. On the side of the lattice model we use the excited-state TBA approach. We consider in detail the case of the descendant at level 8.

Key words: integrable models; six vertex model; XXZ spin chain; fermionic basis, thermodynamic Bethe ansatz; excited states; conformal field theory; Virasoro algebra.

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