The tricritical point of finite - temperature phase transitions in large N ( Higgs ) gauge theories

The tricritical point of finite-temperature phase transitions in large N (Higgs) gauge theories. Abstract Gauge theories broken by a single Higgs field are known to have first-order phase transitions in temperature if λ/g 2 ≪ 1, where g is the gauge coupling and λ the Higgs self-coupling. If the theory is extended from one to N Higgs doublets, with U(N) flavor symmetry, the transition is known to be second order for λ/g 2 > ∼ 1 in the N → ∞ limit. We show that one can in principal compute the tricritical value of λ/g 2 , separating first from second-order transitions, to any order in 1/N. In particular, scalar fluctuations at the transition damp away the usual problems with the infrared behavior of high-temperature non-Abelian gauge theories. We explicitly compute the tri-critical value of λ/g 2 for U(1) and SU(2) gauge theory to next-to-leading order in 1/N. Neither the United States nor the United States Department of Energy, nor any of their employees , nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the product or process disclosed, or represents that its use would not infringe privately-owned rights. By acceptance of this article, the publisher and/or recipient acknowledges the U.S. Government's right to retain a non-exclusive, royalty-free license in and to any copyright covering this paper.