Large-N limit of non-local 2D generalized Yang-Mills theories on non-orientable surface

Abstract

The large-group behavior of the non-local two dimensional generalized Yang-Mills theories (nlgYM${}_2$'s) on arbitrary closed non-orientable surfaces is investigated. It is shown that all order of $\ddot{I}{•}^{2k}$ model of these theories have thired order phase transition only on projective plane (RP${}^2$). Also the phase structure of $\ddot{I}{•}^2+\frac{\hat{I}}{³}4\ddot{I}{•}^4$ model of nlgYM${}_2$ is studied and it is found that for ${\hat{I}}^3>0$, this model has third order phase transition only on RP${}^2$ and for ${\hat{I}}^3<0$ it has third order phase transition on any closed non-orientable surfaces except RP${}^2$ and Klein bottel.

11 pages, no figures, Latex. to be appear in IJMPA