Chiral Symmetry Breaking and Phase Transitions in Holographic Gauge Theories

指導教員: 埼玉大学大学院理工学研究科教授 谷井義彰We discuss the spontaneous breaking of the chiral symmetry in QCD in the framework of the string/gauge duality. We use two different holographic models of QCD. One of them is the general intersecting Dq/Dp brane model consisting of N_c Dq-branes and a single probe Dp-brane. The other is the Dq/Dp-anti-Dp brane model in which we use N_f Dp-anti-Dp-brane pairs as a probe. In particular we consider the D4/D8-anti-D8 configuration. In both models there is an s-dimensional intersection between the Dq-branes and the probe branes. The theory localized at the intersection is an (s + 1)-dimensional QCD-like theory (QCD_<s+1>) in certain cases. In terms of the string/gauge duality we study the dynamics of strongly coupled large N_c QCD_<s+1> at zero and finite temperature (and also at finite chemical potential). The near horizon limit and the probe approximation allow us to treat the Dq-branes as a background geometry and the Dp-brane or Dp-anti-Dp-branes as a probe which does not affect this background. In both models the breaking of the chiral symmetry is closely related to configurations of the probe branes in the Dq background. The quark mass and the quark condensate can be read from the asymptotic behavior of the Dp(-anti-Dp)-brane embedding. In the Dq/Dp model we find that the chiral symmetry is spontaneously broken at zero temperature for certain (q, p, s). We also find that there appear massless Nambu-Goldstone (NG) bosons associated with this spontaneous symmetry breaking. In the D4/D8-anti-D8 model we introduce a chemical potential for the baryon number symmetry as well as temperature. The chemical potential for the baryon number symmetry is introduced as a non-vanishing asymptotic value of the time component of U(1) gauge field on the probe brane. We analyze the phase structure of the model and find a chiral phase transition of the first order