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D3/D7 holographic Gauge theory and Chemical potential

Kazuo Ghoroku, Masafumi Ishihara, Akihiro Nakamura

Abstract

N=2 supersymmetric Yang-Mills theory with flavor hypermultiplets at finite temperature and in the dS${}_4$ are studied for finite quark number density ($n_b$) by a dual supergravity background with non-trivial dilaton and axion. The quarks and its number density $n_b$ are introduced by embedding a probe D7 brane. We find a critical value of the chemical potential at the limit of $n_b=0$, and it coincides with the effective quark mass given in each theory for $n_b=0$. At this point, a transition of the D7 embedding configurations occurs between their two typical ones. The phase diagrams of this transition are shown in the plane of chemical potential versus temperature and cosmological constant for YM theory at finite temperature and in dS${}_4$ respectively. In this phase transition, the order parameter is considered as $n_b$. % and the critical value of the chemical potential This result seems to be reasonable since both theories are in the quark deconfinement phase.

D3/D7 holographic Gauge theory and Chemical potential

Abstract

N=2 supersymmetric Yang-Mills theory with flavor hypermultiplets at finite temperature and in the dS are studied for finite quark number density () by a dual supergravity background with non-trivial dilaton and axion. The quarks and its number density are introduced by embedding a probe D7 brane. We find a critical value of the chemical potential at the limit of , and it coincides with the effective quark mass given in each theory for . At this point, a transition of the D7 embedding configurations occurs between their two typical ones. The phase diagrams of this transition are shown in the plane of chemical potential versus temperature and cosmological constant for YM theory at finite temperature and in dS respectively. In this phase transition, the order parameter is considered as . % and the critical value of the chemical potential This result seems to be reasonable since both theories are in the quark deconfinement phase.

Paper Structure

This paper contains 7 sections, 55 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Background geometry
  3. D7 brane action and equation of motion:
  4. Chemical potential and phase transition
  5. Phase transition at high temperature phase
  6. Phase transition in $dS_4$
  7. Summary

Figures (6)

  • Figure 1: Two embedding solutions for $q=0$, $m_q=1.309, n_b=10^{-5}$ at the critical temperature $T_1=0.45$.
  • Figure 2: Embedding solutions near the transition point for $q=0$, $m_q=1.30916$. The left are for $T=0.4$, and $n_b=$0, 0.000187, 0.00184, 0.0181, 0.217 from the above. The right is for $T=0.8$, and $n_b=$0, 5, 10.
  • Figure 3: Phase diagram in T-$\mu$ plane for R=1,$m_q=1.30916$. The dots represent the effective quark mass $\tilde{m}_q$ given by the last equation (\ref{['qmass']}).
  • Figure 4: The extended small $\mu$ region of the Fig. \ref{['chemical1']} is shown. At first, the two BH embeddings appear on the horizontal line at $(T,\mu,n_b)=(0.450158,0.0223708,0.00699)$ in a degenerated form. Then for decreasing $n_b$, they run on the line in the opposite direction shown by the arrows and approache to the point (a) and (b), which corresponds to the two BH configurations shown in the Fig.\ref{['wq0fig']}.
  • Figure 5: Embedding solutions near the transition point for $q=0$, $m_q=2.94966$. The left are for $\lambda=4$, and $n_b=$0, 0.000124, 0.00124, 0.0133 and 0.0971 from the above. The right is for $\lambda=6$, and $n_b=$0, 0.001, 0.01.
  • ...and 1 more figures