Tricritical point of finite-temperature phase transitions in largeN(Higgs) gauge theories

Abstract

Gauge theories broken by a single Higgs field are known to have first-order phase transitions in temperature if $\ensuremath{\lambda}{/g}^{2}\ensuremath{\ll}1$, where $g$ is the gauge coupling and $\ensuremath{\lambda}$ 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 $\ensuremath{\lambda}{/g}^{2}\ensuremath{\gtrsim}1$ in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. We show that one can, in principle, compute the tricritical value of $\ensuremath{\lambda}{/g}^{2}$, 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 tricritical value of $\ensuremath{\lambda}{/g}^{2}$ for U(1) and SU(2) gauge theory to next-to-leading order in $1/N$.