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Holographic effective theories for strongly coupled physics Shieh , Hsien-Hang


In this thesis we summarize three of our work using the gauge/gravity dualities to build effective theories for strongly coupled phenomena. First, we study the thermodynamics of large N pure 2+1 dimensional Yang-Mills theory on a small spatial S². By studying the effective action for the Polyakov loop order parameter, we show analytically that the theory has a second order deconfinement transition. Our results together with extrapolation of lattice QCD results imply a critical radius in the phase diagram where the deconfinement transition switches from second order to first order. We show that the point at the critical radius and temperature can be either a tricritical point with universal behavior or a triple point separating three distinct phases. Second, we study a model of holographic QCD at zero temperature and finite chemical potential. We find that as the baryon chemical potential is increased, the system transitions to a nuclear matter phase characterized by a condensate of instantons on the probe D-branes in the string theory dual. The electrostatic interactions between the instantons cause the condensate to expand towards the UV with increasing chemical potential, giving a holographic version of the expansion of the Fermi surface. We also find possible explanation of the ``chiral density wave'' instability in large N QCD. We argue that the model can be used to make semi-quantitative predictions of the binding energy per nucleon for nuclear matter in QCD. Third, we consider an Abelian Higgs model placed in an AdS black hole background. Such model has been shown to exhibit superconductor like transitions. In the superconducting phase the system shows infinite DC conductivity. This suggests the possibility of turning on a time independent supercurrent. In this paper we study such supercurrent solutions and the associated phase diagram. We find a critical point in the phase diagram where the second order superconducting transition becomes first order. Supercurrent solutions are well studied in condensed matter systems. We find some qualitative agreement with known results.

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