A holographic critical point

Abstract

We numerically construct a family of five-dimensional black holes exhibiting a line of first-order phase transitions terminating at a critical point at finite chemical potential and temperature. These black holes are constructed so that the equation of state and baryon susceptibilities approximately match QCD lattice data at vanishing chemical potential. The critical endpoint in the particular model we consider has temperature 143 MeV and chemical potential 783 MeV. Critical exponents are calculated, with results that are consistent with mean-field scaling relations.

On finite-temperature holographic QCD in the Veneziano limit

“…A defining characteristic of this class of models is that they contain full backreaction between the duals of the color and flavor degrees of freedom. Earlier work [41][42][43][44][45][46][47][48] on thermodynamics in such bottom-up models imposed quasiconformality directly on the beta function of the theory. One should note that walking behavior and the related "conformal transition" at x f = x c have also been studied in top-down models [49][50][51][52][53][54], as well as in simpler bottom-up models [55][56][57][58][59][60] which do not attempt to model the backreaction.…”

A refined holographic QCD model and QCD phase structure

“…To get a fields configuration which is both consistent with the equation of motions and realizes the linear Regge trajectory, dynamical soft-wall models were constructed by introduce a dilaton potential consistently [10,11]. On the other hand, the Einstein-dilaton and Einstein-Maxwell-dilaton models have been widely studied numerically [12][13][14][15][16] to investigate the thermodynamical properties and explore the phase structure in QCD. Recently, by the potential reconstruction method, analytic solutions have been obtained in the Einstein-dilaton model [17] as well as in the Einstein-Maxwell-dilaton model [16,18].…”

Warped Ricci-flat reductions

“…This does not affect the Ricci scalar, since the above solutions are Ricci-flat, but it does show up in contractions of the Riemann tensor R M N P Q R M N P Q . This singularity can be seen to be of "good" type [8], a point that was made recently in [16] and we will return to in due course. In contrast, the Minkowski and de Sitter solutions are smooth.…”

“…In this section, we offer an explanation as to why that may be the case. Our observation hinges on a known "far from BPS" near-horizon limit of certain extremal black holes in D = 4 U(1) 4 and D = 5 U(1) 3 gauged supergravity [13,14] (see also [16]), where an AdS 3 near-horizon is formed by incorporating an internal circular direction with the scalars, in this case X i , all scaled appropriately.…”

“…Within an AdS/CFT context, such warped-product solutions have been studied previously in [13,14] (more recently [15,16]), where consistent KK reductions to lower-dimensional theories were constructed. In contrast to usual AdS/CFT setups, the vacua of the lower-dimensional theories are supported exclusively through the warp factor and lift to vacuum solutions in ten and eleven dimensions.…”