Large-N limit of the generalized 2-dimensional Yang-Mills theories

Abstract

Using the standard saddle-point method, we find an explicit relation for the large-N limit of the free energy of an arbitrary generalized 2D Yang-Mills theory in the weak ($A<A_c$) region. In the strong ($A>A_c$) region, we investigate carefully the specific fourth Casimir theory, and show that the ordinary integral equation of the density function is not adequate to find the solution. There exist, however, another equation which restricts the parameters. So one can find the free energy in strong region and show that the theory has a third order phase transition.

10 pages, minor typos corrected, one reference updates

Cited by in corpus (15)

• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Uniqueness of the minimum of the free energy of the 2D Yang-Mills theory at large N
• Nonlocal two-dimensional Yang-Mills- and generalized Yang-Mills-theories
• Large-N limit of the two-dimensoinal Yang-Mills theory on surfaces with boundaries
• Large-N behavior of the Wilson loops of generalized two-dimensional Yang-Mills theories
• More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM${}_2$'s)
• Phase transitions of Large-N two-dimensional Yang-Mills and generalized Yang-Mills theories in the double scaling limit
• Large-N limit of the generalized 2D Yang-Mills theory on cylinder
• Generalized simplicial chiral models
• Large-N transitions for generalized Yang-Mills theories in 1+1 dimensions
• Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories
• Non-local 2D Generalized Yang-Mills theories on arbitrary surfaces with boundary
• More on generalized simplicial chiral models
• Large-N limit of the two-dimensinal Non-Local Yang-Mills theory on arbitrary surfaces with boundary