Vacuum energy of the BukhvostovLipatov model
Abstract
Bukhvostov and Lipatov have shown that weakly interacting instantons and antiinstantons in the O (3) nonlinear sigma model in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. We propose an exact formula for the vacuum energy of the model for twisted boundary conditions, expressing it through a special solution of the classical sinhGordon equation. The formula perfectly matches predictions of the standard renormalized perturbation theory at weak couplings as well as the conformal perturbation theory at short distances. Our results also agree with the Bethe ansatz solution of the model. A complete proof the proposed expression for the vacuum energy based on a combination of the Bethe ansatz techniques and the classical inverse scattering transform method is presented in the second part of this work [42].
 Publication:

Nuclear Physics B
 Pub Date:
 October 2016
 DOI:
 10.1016/j.nuclphysb.2016.08.031
 arXiv:
 arXiv:1607.04839
 Bibcode:
 2016NuPhB.911..863B
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematical Physics
 EPrint:
 28 pages, 10 figures