Phase structure of the generalized two-dimensional Yang-Mills theory on sphere

M. Alimohammadi; A. Tofighi

doi:doi:10.1007/s100529900009

EPJ

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 8, 711-717
DOI 10.1007/s100529900009

Phase structure of the generalized two-dimensional Yang-Mills theory on sphere

M. Alimohammadi¹ - A. Tofighi^2,3

¹ Department of Physics, University of Tehran, North-Kargar Ave., Tehran, Iran
² Department of Physics, University of Mazandaran, Babolsar, Iran
³ Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran

Received: 30 September 1998 / Revised version: 13 December 1998 / Published online: 15 April 1999

Abstract
We find a general expression for the free energy of $G(\phi )=\phi^{2k}$ generalized two-dimensional (2D) Yang-Mills theory in the strong (A>A_c) region for large N. We also show that in this region, the density function of Young tableau of these models is a three-cut problem. In the specific $\phi^6$ model, we show that the theory has a third order phase transition, like the $\phi^2$ (YM₂) and $\phi^4$ models. We note problems for cases where $k \geq 4$ , and at the end, examine the phase structure of the $\phi^2 + g \phi^4$ model for the $g \leq {A/4}$ region.