Dissolved deconfinement: Phase structure of large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>gauge theories with fundamental matter

Abstract

A class of large $N$ $U(N)$ gauge theories on a compact manifold ${S}^{3}\ifmmode\times\else\texttimes\fi{}\mathbb{R}$ (with possible inclusion of adjoint matter) is known to show first-order deconfinement transition at the deconfinement temperature. This includes the familiar example of pure $YM$ theory and $\mathcal{N}=4$ Supersymmetric Yang-Mills theory. Here we study the effect of introduction of ${N}_{f}$ fundamental matter fields in the phase diagram of the above mentioned gauge theories at small coupling and in the limit of large $N$ and finite ${N}_{f}/N$. We find some interesting features like the termination of the line of first-order deconfinement phase transition at a critical point as the ratio ${N}_{f}/N$ is increased and absence of deconfinement transition thereafter (there is only a smooth crossover). This result may have some implication for QCD, which unlike a pure gauge theory does not show a first-order deconfinement transition and only displays a smooth crossover at the transition temperature.