Transitions in dilaton holography with global or local symmetries
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- Salvio, A. J. High Energ. Phys. (2013) 2013: 136. doi:10.1007/JHEP03(2013)136
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We study various transitions in dilaton holography, including those associated with the spontaneous breaking of a global (superfluid case) or local (superconductor case) U(1) symmetry in diverse dimensions d. By analyzing the thermodynamics of the dilaton-gravity system we find that scale invariance is broken at low temperatures, as shown by a nontrivial hyperscaling violation exponent in the infrared; increasing the temperature we recover scale symmetry in a d dependent way: while for d = 2 + 1 a phase transition is found, for d = 3 + 1 the transition is rather a crossover. This is the expected behavior of QCD where the number of colors Nc equals three (although in our holographic calculations Nc → ∞). When the U(1) is preserved and at low temperatures, the system is insulating for arbitrary d if the dilaton is appropriately coupled to the gauge field; for other couplings we also find a linear in temperature resistivity. We then determine the prediction of these models for several quantities in the superconducting phase: the DC and AC conductivity, the gap for charged excitations, the superfluid density, the vortex profiles, the coherence length, the penetration depth and the critical magnetic fields. We show that at low temperatures some of these quantities differ qualitatively compared with the corresponding models without the dilaton, although the superconductor is robustly of Type II. The ratio of the gap over the critical temperature of the superconductor is studied in detail varying d and the couplings of the dilaton and then compared with the BCS value. A holographic renormalization is required in d > 2 + 1 to compute some quantities (such as the AC conductivity and the penetration depth) and we explain in detail how to perform it.