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

TL;DR

This paper analyzes the large-N behavior of non-local 2D generalized Yang-Mills theories on non-orientable surfaces, revealing specific phase transition orders depending on the surface topology and model parameters.

Contribution

It demonstrates that all even-power models exhibit third-order phase transitions only on the projective plane and explores the phase structure of a specific model with quartic interaction.

Findings

Third-order phase transition occurs only on RP^2 for all even-power models.

In the $^2 + rac{g}{4}^4$ model, transition order depends on $g$ and surface topology.

Transitions are absent on Klein bottle for certain parameter ranges.

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 $\phi^{2k}$ model of these theories have thired order phase transition only on projective plane (RP$^2$). Also the phase structure of $\phi^2 + \frac{\gamma}{4}\phi^4$ 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.