Phase transition of generalized two dimensional Yang-Mills U(N) on the sphere for $G(z)=z^4+\lambda\,z^3$ and Maxwell construction

TL;DR

This paper studies the phase transitions in a generalized 2D Yang-Mills theory on a sphere, revealing two phase transitions of different orders and connecting mathematical properties to four-dimensional space-time.

Contribution

It identifies and characterizes two distinct phase transitions in the generalized Yang-Mills model with a specific polynomial potential, and relates 2D mathematical structures to 4D space-time.

Findings

Two phase transitions: one third order, one second order

Comparison between gYM_2 and Maxwell construction

Established a mathematical link to four-dimensional space-time

Abstract

The large-N behavior of the quartic-cubic generalized two dimensional Yang-Mills U(N) on the sphere is investigated for finite cubic couplings. First, it is shown that there are two phase transitions one of which is third order and the other one is second order. Second, $gYM_2$ and Maxwell construction are compared and a relationship between two-dimensional space-time, that is purely mathematical, and four-dimensional space-time is obtained.