The holographic quantum effective potential at finite temperature and density

We develop a formalism that allows the computation of the quantum effective potential of a scalar order parameter in a class of holographic theories at finite temperature and charge density. The effective potential is a valuable tool for studying the ground state of the theory, symmetry breaking patterns and phase transitions. We derive general formulae for the effective potential and apply them to determine the phase transition temperature and density in the scaling region.Comment: 27 page

On the sign of the dilaton in the soft wall models

We elaborate on the existence of a spurious massless scalar mode in the vector channel of soft-wall models with incorrectly chosen sign of the exponential profile defining the wall. We re-iterate the point made in our earlier paper and demonstrate that the presence of the mode is robust, depending only on the infra-red asymptotics of the wall. We also re-emphasize that desired confinement properties can be realized with the correct sign choice.Comment: 10 page

Generalized Holographic Quantum Criticality at Finite Density

We show that the near-extremal solutions of Einstein-Maxwell-Dilaton theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions. This explains the scaling of their thermodynamic functions and their IR transport coefficients, the nature of their spectra, the Gubser bound, and regulates their singularities. We propose that these are the most general quantum critical IR asymptotics at finite density of EMD theories.Comment: v4: Corrected the scaling equation for the conductivity in section 9.

Quantum critical lines in holographic phases with (un)broken symmetry

All possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified. Scale invariant geometries where the scalar extremizes its effective potential are distinguished from hyperscaling violating geometries where the scalar runs logarithmically. It is shown that the general critical saddle-point solutions are characterized by three critical exponents ($\theta, z, \zeta$). Both exact solutions as well as leading behaviors are exhibited. Using them, neutral or charged geometries realizing both fractionalized or cohesive phases are found. The generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale invariant solutions with a constant scalar.Comment: v3: 32+29 pages, 2 figures. Matches version published in JHEP. Important addition of an exponent characterizing the IR scaling of the electric potentia

New Insights into Properties of Large-N Holographic Thermal QCD at Finite Gauge Coupling at (the Non-Conformal/Next-to) Leading Order in N

In the context of [1]'s string theoretic dual of large-N thermal QCD-like theories at finite gauge/string coupling (as part of the `MQGP' limit of [2]), we discuss the following. First, up to LO in N, using the results of [3], we show that the local T^3 of [2] is the T^2-invariant sLag of [3] in a resolved conifold. This, together with the results of [4], shows that for a (predominantly resolved or deformed) resolved warped deformed conifold, the local T^3 of [2] in the MQGP limit, is the T^2-invariant sLag of [3] justifying the construction of the delocalized SYZ type IIA mirror of the type IIB background of [1]. Then, using the prescription of [5], we obtain the temperature dependence of the thermal (and electrical) conductivity working up to leading order in N (the number of D3-branes), and upon comparison with [6] show that the results mimic a 1+1-dimensional Luttinger liquid with impurities. Further, including sub-leading non-conformal terms in the metric determined by M (the number of fractional D-branes = the number of colors = 3 in the IR after the end of a Seiberg duality cascade), by looking at respectively the scalar, vector and tensor modes of metric perturbations and using [7]'s prescription of constructing appropriate gauge-invariant perturbations, we obtain respectively the speed of sound, the diffusion constant and the shear viscosity \eta (and \eta/s) including the non-conformal O((g_s M^2) (g_s N_f)/N<<1)-corrections, N_f being the number of flavor D7-branes.Comment: 1+75 pages, LaTeX; Some corrections in Tc-related calculations, results unchange

Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate

The transverse part of the vector-axial vector flavor current correlator in the presence of weak external electric field is studied using holography. The correlator is calculated using a bottom-up model arxiv:1003.2377 {proposed recently}, that includes the non-linear dynamics of the chiral condensate. It is shown that for low momenta the result agrees with the relation proposed by arXiv:1010.0718 {Son and Yamamoto} motivated by a simpler holographic model. For large Euclidean momenta however, the two results diverge. In the process, the difference of the vector and axial vector two point functions is also calculated. At large Euclidean momenta it is found that the first non-perturbative contribution, decreases as $q^{-6}$ as expected from QCD.Comment: 17 pages, 5 figures, typos correcte

Effective Holographic Theories for low-temperature condensed matter systems

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents $(\gamma,\delta)$ that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the $(\gamma,\delta)$ plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when $\gamma=\delta$ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole $(\gamma,\delta)$ plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T=0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.Comment: (v3): Added discussion on the UV completion of the solutions, and on extremal spectra in the charged case. Expanded discusion on insulating extremal solutions. Many other refinements and corrections. 126 pages. 48 figure