Abstract
We investigate consistent charged black hole solutions to the Einstein-Maxwell-Dilaton (EMD) equations that are asymptotically AdS. The solutions are gravity duals to phases of a non-conformal plasma at finite temperature and density. For the dilaton we take a quadratic ansatz leading to linear confinement at zero temperature and density. We consider a grand canonical ensemble, where the chemical potential is fixed, and find a rich phase diagram involving the competition of small and large black holes. The phase diagram contains a critical line and a critical point similar to the van der Waals-Maxwell liquid-gas transition. As the critical point is approached, we show that the trace anomaly in the plasma phases vanishes signifying the restoration of conformal symmetry in the fluid. We find that the heat capacity and charge susceptibility diverge as $C_V \propto (T-T^c)^{-\alpha}$ and $\chi \propto (T-T^c)^{-\gamma}$ at the critical point with universal critical exponents $\alpha=\gamma=2/3$. Our results suggest a description of the thermodynamics near the critical point in terms of catastrophe theories. In the limit $\mu \to 0$ we compare our results with lattice results for $SU(N_c)$ Yang-Mills theories.
Highlights
Matter under extreme conditions is an exciting and challenging research field in high-energy physics
We find in this work a critical line in the T-μ phase diagram, associated with the first-order transition, that ends on a critical end point (CEP)
We show explicitly the following results: (i) Conformal symmetry is explicitly broken at μ 1⁄4 0 due to the deformation of the 4D theory, dual to the dilaton backreaction to the AdS black brane. (ii) Conformal symmetry breaking due to the dilaton backreaction persists at finite μ, and the trace anomaly E − 3p is in general nonzero. (iii) As we reach the critical point in the T-μ phase diagram, the trace anomaly goes to zero
Summary
Matter under extreme conditions is an exciting and challenging research field in high-energy physics. Several other studies followed, dealing with different aspects of the thermodynamics, including phase transitions between different black hole branches and a quantitative comparison with lattice QCD results for some holographic models [33,34,35,36,37,38,39,40,41,42] In these works, universal aspects of charged black holes in EMD holography were not investigated. We find universal critical exponents for the specific heat and charge susceptibility These results hold for any holographic model, based on EMD theory with a minimal coupling, displaying a critical line that ends on a CEP as the chemical potential increases. Appendix B describes an alternative method for reconstructing the grand canonical potential, and Appendix C describes the charge susceptibility in our model
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