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 ${\varphi }^{2k}$ model of these theories have thired order phase transition only on projective plane (RP${}^2$). Also the phase structure of ${\varphi }^2+\frac{\gamma }{4}{\varphi }^4$ model of nlgYM${}_2$ is studied and it is found that for $\gamma >0$, this model has third order phase transition only on RP${}^2$ and for $\gamma <0$ it has third order phase transition on any closed non-orientable surfaces except RP${}^2$ and Klein bottel.

arXiv comment11 pages, no figures, Latex. to be appear in IJMPA

References in corpus (15)

• Two Dimensional Gauge Theories Revisited
• Two Dimensional QCD is a String Theory
• Two Dimensional QCD as a String Theory
• The String Theory Approach to Generalized 2D Yang-Mills Theory
• Summing Over Inequivalent Maps in the String Theory Interpretation of Two Dimensional QCD
• Large N Phase Transitions and Multi-Critical Behaviour in Generalized 2D QCD
• Wilson Loops in Large N QCD on a Sphere
• Uniqueness of the minimum of the free energy of the 2D Yang-Mills theory at large N
• $n$-point functions of $2d$ Yang-Mills theories on Riemann surfaces
• Phase structure of the generalized two dimensional Yang-Mills theories on sphere
• Nonlocal two-dimensional Yang-Mills- and generalized Yang-Mills-theories
• On the phase structure of two--dimensional generalized Yang--Mills theories
• Large-N limit of the non-local 2D Yang-Mills and generalized Yang-Mills theories on a cylinder
• More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM${}_2$'s)
• Generating Functional and Large N-Limit of Nonlocal 2D Generalized Yang-Mills Theories ($nlgY{M}_2$'s)