Speaker
Description
The two-dimensional Principal Chiral Model (PCM) has been considered since long as an instructive example of a QFT bearing certain similarities with QCD: asymptotic freedom, dimensional transmutation with a physical mass spectrum and a non-trivial 't Hooft's large N limit. In addition, it is an integrable QFT, with the known physical S-matrix. In our 1994 paper with V.Fateev and P.Wiegmann, we found not only the exact but also explicit solution of the vacuum energy of SU(N)xSU(N) PCM in the 't Hooft limit in the presence of specific, albeit arbitrary strong, "magnetic" field (the chemical potential of density of physical particles). The shape of this field repeated the Perron-Frobenius (PF) mode on the su(N) Dynkin diagram. I will present our recent work with E.Sobko and K.Zarembo (arxiv:2312.04801) where we explicitly solved the Bethe equation for the magnetic field of arbitrary shape. We also studied this solution in the case of small deviations of the magnetic field from the PF mode and found a perfect correspondence with the known perturbative and strong coupling results. I will also mention our results of our previous work: the 1/N expansion of the energy and a possible interpretation of PCF as a 2+1-dimensional noncritical string theory, where the role of the 3rd dimension is played by Dynkin diagram.
