Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-12-30
JHEP 0912:060,2009
Physics
High Energy Physics
High Energy Physics - Theory
51 pages, 7 figures; typos corrected, accepted for publication in JHEP
Scientific paper
10.1088/1126-6708/2009/12/060
We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic Bethe ansatz equations of Yang and Yang. It is derived from the Zamolodchikov scattering theory in the cross channel, for virtual particles along the non-compact direction of the space-time cylinder. The method is based on the integrable Hirota dynamics that follows from the Y-system. The outcome is a nonlinear integral equation for a single complex function, valid for an arbitrary quantum state and accompanied by the finite size analogue of Bethe equations. It is close in spirit to the Destri-deVega (DdV) equation. We present the numerical data for the energy of various states as a function of the size, and derive the general Luscher-type formulas for the finite size corrections. We also re-derive by our method the DdV equation for the SU(2) chiral Gross-Neveu model.
Gromov Nikolay
Kazakov Vladimir
Vieira Pedro
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