Physics Letters B 778 (2018) 419–425
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Holographic QCD phase diagram with critical point
from Einstein–Maxwell-dilaton dynamics
J. Knaute
a,b,∗
, R. Yaresko
a,b
, B. Kämpfer
a,b
a
Helmholtz-Zentrum Dresden-Rossendorf, POB 51 01 19, 01314 Dresden, Germany
b
TU Dresden, Institut für Theoretische Physik, 01062 Dresden, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
24 February 2017
Received
in revised form 27 October 2017
Accepted
18 January 2018
Available
online xxxx
Editor:
J.-P. Blaizot
Keywords:
Gravity
dual
Holography
Quark–gluon
plasma
Critical
point
Supplementing the holographic Einstein–Maxwell-dilaton model of [1,2] by input of lattice QCD data for
2 + 1flavors and physical quark masses for the equation of state and quark number susceptibility at
zero baryo-chemical potential we explore the resulting phase diagram over the temperature-chemical
potential plane. A first-order phase transition sets in at a temperature of about 112 MeV and a baryo-
chemical
potential of 612 MeV. We estimate the accuracy of the critical point position in the order of
approximately 5–8% by considering parameter variations and different low-temperature asymptotics for
the second-order quark number susceptibility. The critical pressure as a function of the temperature has
a positive slope, i.e. the entropy per baryon jumps up when crossing the phase border line from larger
values of temperature/baryo-chemical potential, thus classifying the phase transition as a gas–liquid one.
The updated holographic model exhibits in- and outgoing isentropes in the vicinity of the first-order
phase transition.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
The QCD phase diagram exhibits potentially a large variety of
structures [3–6]. Either originating from extrapolations of weak-
coupling
results or being suggested by models (most notably
Nambu–Jona–Lasinio (cf. [7]), linear sigma/quark-meson [8] mod-
els
in numerous variants), various phases of strongly interacting
matter may occur, such as color superconductors (cf. [9–11]), or
quarkyonic matter (cf. [12]), or chirally restored phases (cf. [13]),
or color-flavor locked structures (cf. [14]).
While
the gas–liquid (GL) first-order phase transition (FOPT)
in nuclear matter seems to be well established since some time
[15–20], the hadron–quark (HQ) deconfinement transition still of-
fers
a few challenges. At very small or zero net-baryon density
corresponding to a small chemical potential (μ)-to-temperature
(T ) ratio, μ/T 1, the HQ transition is established as a crossover
in 2 + 1flavor lattice QCD with physical quark masses [21,22] at
a characteristic scale of T
c
= O(150 MeV). The popular Columbia
plot [23] sketches qualitatively the options of the phase structure
in dependence of the u, d, s quark masses m
u,d,s
. For instance, in
the chiral limit, m
u,d,s
→0, or the opposite infinitely heavy quark-
*
Corresponding author.
E-mail
address: j.knaute@hzdr.de (J. Knaute).
mass limit, m
u,d,s
→∞, the deconfinement transition is a FOPT.
Due to the sign problem of the fermionic determinant the ab initio
lattice QCD evaluations are not yet conclusive with respect to the
confinement and chiral restoration transition(s) at non-zero baryo-
chemical
potential, in particular for μ/T > 2. Some methods try
to avoid or circumvent the sign problem (cf. [24]), e.g. by evalu-
ations
at imaginary μ (which need a prescription of iμ → μ) or
a Taylor expansion in powers of μ/T with coefficients calculated
at μ = 0 (which needs statements on the convergence [25]), or
the reweighting method (which needs statements on the density
and parameter ranges to incorporate the sign and overlap prob-
lem [26]).
Other approaches are based on the complex Langevin
method [27,28] (see [29] for recent developments) or a recent pro-
posal
for a path optimization method [30], which is based on the
Lefschetz-thimble path-integral method [31].
The
pertinent uncertainties make the region of larger μ/T in-
teresting.
A particularly interesting option is the possibility of a
(critical) end point (CEP) of a curve of FOPTs, e.g. T
c
(μ), setting in
at (T
CEP
, μ
CEP
) and running toward the T = 0axis when imaging
the phase diagram in the T –μ plane.
The
CEP coordinates are yet fairly unconstrained. Plugging
model results and QCD-related extrapolations together one arrives
at some less conclusive scatter plot (cf. e.g. [24]). Advanced lattice
QCD approaches disfavor a CEP position at T /T
c
(μ =0) > 0.9 and
μ/T ≤2 [25].
https://doi.org/10.1016/j.physletb.2018.01.053
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.