Principal chiral field at large N
Abstract
We present an exact and explicit solution of the principal chiral field in two dimensions for a group manifold with infinitely large rank. The energy of the ground state is explicitly found for the external Noether fields of arbitrary magnitude. The exact GellMannLow function exhibits asymptotic freedom behaviour at large value of the field in agreement with perturbative calculations. Coefficients of the perturbative expansion in the renormalized charge are calculated. They grow factorially with the order showing the presence of renormalons. At small field we found an inverse logarithmic singularity in the groundstate energy at the mass gap which indicates that at N = ∞ the spectrum of the theory contains extended objects rather than pointlike particles.
 Publication:

Nuclear Physics B
 Pub Date:
 August 1994
 DOI:
 10.1016/05503213(94)904057
 arXiv:
 arXiv:hepth/9403099
 Bibcode:
 1994NuPhB.424..505F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 19 pages, preprint ENS94/07, LATEX