Abstract
A holographic bottom-up model used in studying the superconducting system is applied to search for the color superconducting phase of supersymmetric Yang-Mills theory. We apply the probe analysis of this model to the supersymmetric Yang-Mills theory in both the confinement and deconfinement phases. In this analysis, we find the color superconductivity in both phases when the baryon chemical potential exceeds a certain critical value. This result implies that, above the critical chemical potential, a color non-singlet diquark operator, namely the Cooper pair, has its vacuum expectation value even in the confinement phase. In order to improve this peculiar situation, we proceed the analysis by taking account of the full back-reaction from the probe. As a result, the color superconducting phase, which is observed in the probe approximation, disappears in both the confinement and deconfinement phases when parameters of the theory are set within their reasonable values.
Highlights
The color superconducting (CSC) phase has been expected in QCD at the finite baryon chemical potential, but it is difficult to show it
We have studied a possibility of the CSC phase in the supersymmetric Yang-Mills (SYM) theory by using a bottom-up holographic model which is constructed by the gravity and a simple matter action composed of a Uð1Þ gauge field and a charged scalar
The mass and the charge of the scalar give the conformal dimension and the baryon number of the composite operator of the dual SYM theory. It is chosen as a scalar which is dual to the diquark operator
Summary
The color superconducting (CSC) phase has been expected in QCD at the finite baryon chemical potential, but it is difficult to show it (see e.g., the review [1]). The charged scalar is dual to a composite field operator with a finite quark number In the model, they are not introduced through the probe D-branes but are given by the bulk action. In order to improve the probe approximation, it is natural to consider the vacuum solutions which are given by solving the Einstein-Maxwell equation of the system with the Einstein-Hilbert action and the Uð1Þ gauge field part In this case, the phase diagram in the μ-T plane should be modified to the chemical potential dependent form.. The phase diagram in the μ-T plane should be modified to the chemical potential dependent form.2 This modification is equivalently obtained by taking account of the full backreaction from the probe action as shown in Ref.
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