Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics

Understand

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.