Anti-de Sitter Space/conformal Field Theory Research Articles

Pole-skipping of holographic correlators: aspects of gauge symmetry and generalizations

In the framework of anti-de Sitter space/conformal field theory (AdS/CFT), we study the pole-skipping phenomenon of the holographic correlators of boundary operators. We explore the locations of the pole-skipping points case by case with the U(1)-gauged form models in the asymptotic AdS bulk of finite temperature. In general, in different cases all the points are located at the Matsubara frequencies with corresponding wave vectors dispersed in the momentum space, displaying different types of patterns. Specifically, in the massless cases with U(1) symmetry, the wave vectors of the pole-skipping points have a form-number dependence, and a trans-mode equivalence in the dual fields is found in correspondence with electromagnetic duality. In the massive cases with explicit symmetry breaking, the points degenerate to be independent of the form number. We expect in such kind of pole-skipping properties implications of distinctive physics in the chaotic systems. These properties are further examined by higher-order computation, which provides a more complete pole-skipping picture. Our near-horizon computation is verified with the double-trace method especially in the example of 2-form where there is dimension-dependent boundary divergence. We illustrate in these cases that the pole-skipping properties of the holographic correlators are determined by the IR physics, consistent with the ordinary cases in previous studies.

Bottomonia suppression in heavy-ion collisions from anti–de Sitter space/conformal field theory

We compute for the first time the suppression of bottomonia in a strongly coupled quark-gluon plasma (QGP) and compare the results to those from a weakly coupled QGP. Using imaginary time techniques we numerically determine the real and imaginary parts of the ground-state binding energy of the bottomonia in one potential computed from anti--de Sitter space/conformal field theory (AdS/CFT) and another computed from perturbative quantum chromodynamics. We confirm the strong-coupling binding energies by independently deriving the meson spectrum in AdS/CFT using semiclassical, rotating open strings. We then use these binding energies in a suppression model to determine the $\mathrm{\ensuremath{\Upsilon}}$(1S) nuclear modification factor in ${\sqrt{s}}_{NN}=2.76$-TeV $\mathrm{Pb}+\mathrm{Pb}$ collisions. AdS/CFT significantly overpredicts the suppression compared to data, although the predictive power of our calculation is limited by its significant sensitivity to the exact details of the suppression model.

Holographic interpretation of Shannon entropy of coherence of quantum pure states

For a quantum pure state in conformal field theory, we generate the Shannon entropy of its coherence, that is, the von Neumann entropy obtained by introducing quantum measurement errors. We give a holographic interpretation of this Shannon entropy, based on Swingle's interpretation of anti-de Sitter space/conformal field theory (AdS/CFT) correspondence in the context of AdS3/CFT2. As a result of this interpretation, we conjecture a differential geometrical formula for the Shannon entropy of the coherence of a quantum pure or purified state in CFT2 at thermal and momentum equilibrium as the sum of the holographic complexity and the abbreviated action, divided by πℏ, in the bulk domain enclosed by the Ryu-Takayanagi curve. This result offers a definition of the action of a bulk model of qubits dual to the boundary CFT2 at this equilibrium.

Bañados–Teitelboim–Zanelli Black Hole in the Information Geometry

We examine the Banados-Teitelboim-Zanelli (BTZ) black hole in terms of the information geometry and consider what kind of quantum information produces the black hole metric in close connection with the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. We find a Hessian potential that exactly produces both the BTZ metric and the entanglement entropy formula for CFT_{1+1} at a finite temperature. Taking a free-falling frame near the event horizon is a key procedure to derive these exact results. We also find an alternative Hessian potential that produces the same BTZ metric, which is found using the duality relation based on the Legendre transformation. We realize that the dual representation originates from the entanglement Hamiltonian on the CFT side. Our results suggest that the present information-geometrical approach is very powerful for understanding the mechanism of the holographic renormalization group such as the AdS/CFT correspondence.

Dynamical three-field AdS/QCD model

The Anti-de Sitter Space/Conformal Field Theory (AdS/CFT) correspondence may offer new and useful insights into the non-perturbative regime of strongly coupled gauge theories such as Quantum Chromodynamics (QCD). We present an AdS/CFT-inspired model that describes the spectra of light mesons. The conformal symmetry is broken by a background dilaton field, and chiral symmetry breaking and linear confinement are described by a chiral condensate field. These background fields, along with a background glueball condensate field, are derived from a potential. We describe the construction of the potential, and the calculation of the meson spectra, which match experimental data well. We argue that the presence of the third background field is necessary to properly describe the meson spectra.

Three-field potential for soft-wall AdS/QCD

The Anti-de Sitter Space/Conformal Field Theory (AdS/CFT) correspondence may offer new and useful insights into the non-perturbative regime of strongly coupled gauge theories such as Quantum Chromodynamics (QCD). Soft-wall AdS/QCD models have reproduced the linear Regge trajectories of meson spectra by including background dilaton and chiral condensate fields. Efforts to derive these background fields from a scalar potential have so far been unsuccessful in satisfying the UV boundary conditions set by the AdS/CFT dictionary while reproducing the IR behavior needed to obtain the correct meson spectra. We present work toward a three-field scalar potential that includes the dilaton field and the chiral and glueball condensates. This model is consistent with background fields that yield linear trajectories for the meson spectra and the correct mass-splitting between the vector and axial-vector mesons.

Pseudoscalar mass spectrum in a soft-wall model of AdS/QCD

The anti--de Sitter space/conformal field theory (AdS/CFT) correspondence may offer new and useful insights into the nonperturbative regime of strongly coupled gauge theories such as quantum chromodynamics (QCD). Recently, a modified soft-wall AdS/QCD model incorporated independent sources for explicit and spontaneous chiral symmetry breaking and linear confinement. This model contains a modified dilaton and higher-order interaction terms in the Lagrangian. Within this model we explore the radial pseudoscalar mass spectrum using two different representations of the pion field. We find the mass eigenvalues associated with each representation show the equivalence between the two, and we find good agreement with the pion masses. The Gell-Mann--Oakes--Renner (GOR) relation is naturally obtained.

Conformal holography of bulk elliptic flow and heavy-quark quenching in relativistic heavy ion collisions

We show that the ``perfect fluid'' elliptic flow of the bulk hadrons and the unexpectedly strong quenching of heavy quark jet fragments in Au $+$ Au reactions at $200A$ GeV can be simultaneously accounted for within leading-order anti-de-Sitter space/conformal field theory (AdS/CFT) holography with a common large t'Hooft coupling $\ensuremath{\lambda}={g}_{\mathit{YM}}^{2}{N}_{c}~30$. In contrast, weakly coupled quark-gluon plasma models have so far failed to describe the observed correlation between these soft and hard observables even for couplings extrapolated to ${\ensuremath{\alpha}}_{s}~0.5$. We show that phenomenological applications of the classical trailing string AdS/CFT holographic solution are furthermore remarkably robust to higher-order curvature corrections $\mathcal{O}(1/{\ensuremath{\lambda}}^{3/2})$ in type IIB supergravity theories, as well as to worldsheet fluctuation corrections $\mathcal{O}(1/{\ensuremath{\lambda}}^{1/2})$ that were not considered previously. We emphasize the importance of future measurements at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) of the correlation between identified charm and beauty quark hard (${p}_{T}>10\ensuremath{-}30$ GeV) jet quenching observables and low transverse momenta (${p}_{T}\ensuremath{\leqslant}1$ GeV) bulk elliptic flow observables to further test the limits of the applicability of conformal holography to strongly coupled quark-gluon plasma.

Diffractive deep inelastic scattering in an AdS/CFT inspired model: A phenomenological study

The analytical treatment of the nonperturbative QCD dynamics is one of main open questions of the strong interactions. Currently, it is only possible to get some qualitative information about this regime considering other QCD-like theories, as for example the N=4 super Yang-Mills (SYM), where one can perform calculations in the nonperturbative limit of large 't Hooft coupling using the Anti-de Sitter space/Conformal field theory (AdS/CFT). Recently, the high energy scattering amplitude was calculated in the AdS/CFT approach, applied to deep inelastic scattering (DIS) and confronted with the $F_2$ HERA data. In this work we extend the nonperturbative AdS/CFT inspired model for diffractive processes and compare its predictions with a perturbative approach based on the Balitsky - Kovchegov (BK) equation. We demonstrate that the AdS/CFT inspired model is not able to describe the current $F_2^{D(3)}$ HERA data and predicts a similar behavior to that from BK equation in the range $10^{-7} \lesssim x_{IP} \lesssim 10^{-4}$. At smaller values of $x_{IP}$ the diffractive structure function is predicted to be energy independent.

Holographic entanglement entropy: an overview

In this paper, we review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. In general, the AdS/CFT relates physical observables in strongly coupled quantum many-body systems to certain classical quantities in gravity plus matter theories. In the case of our holographic entanglement entropy, its gravity dual turns out to be purely geometric, i.e. the area of minimal area surfaces in AdS spaces. One interesting application is to study various phase transitions by regarding the entanglement entropy as order parameters. Indeed we will see that our holographic calculations nicely reproduce the confinement/deconfinement transition. Our results can also be applied to understanding the microscopic origins of black hole entropy.

Early Time Dynamics in Heavy Ion Collisions from CGC and from AdS/CFT

We review two different theoretical approaches to the strong interaction dynamics at the early times immediately following heavy ion collisions. One approach is based on small-coupling physics of the Color Glass Condensate (CGC). The other approach is based on Anti-de Sitter space/Conformal Field Theory (AdS/CFT) correspondence and may be applicable to describing large-coupling QCD interactions. We point out that in terms of theoretical tools the two approaches are somewhat similar: in CGC one deals with classical gluon fields produced in a nuclear shock wave collision, while in AdS/CFT one studies classical gravity in a gravitational shock wave collision. We stress, however, that the resulting physics is different: the classical gluon fields in CGC lead to a free-streaming medium produced in heavy ion collisions, while the classical gravity in the 5-dimensional AdS bulk is likely to lead to ideal hydrodynamics description of the produced medium. Also, the valence quarks in colliding nuclei in CGC continue along their light cone trajectories after the collision with very little recoil, while we show that in AdS the colliding nuclei are likely to lose most of their energy in the collision and stop.

Langevin + Hydrodynamics Approach to Heavy Quark Propagation and Correlation in QGP

We develop a relativistic Langevin dynamics under the background of strongly interacting quark-gluon fluid described by the (3+1)-dimensional hydrodynamics. The drag force acting on charm and bottom quarks is parametrized according to the formula obtained from the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. In this setup, we calculate the nuclear modification factor R AA for the single-electrons from the charm and bottom quarks to extract the magnitude of the drag force from the PHENIX and STAR data. The R AA for single-electrons with p T ⩾ 3 GeV indicates that the drag force is close to the AdS/CFT prediction. Effects of the drag force on the elliptic flow of single-electrons are also discussed. Moreover, we predict the electron-muon correlation which is closely related to the heavy-quark pair correlation in hot matter.

Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid

The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in It\^o discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor ${R}_{\mathrm{AA}}$ and the elliptic flow ${v}_{2}$ for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The ${R}_{\mathrm{AA}}$ for electrons with large transverse momentum (${p}_{T}>3$ GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.

Shear-Viscosity to Entropy-Density Ratio of a Relativistic Hadron Gas

Ultrarelativistic heavy-ion collisions at the Brookhaven National Laboratory Relativistic Heavy Ion Collider (RHIC) are thought to have produced a state of matter called the quark-gluon plasma, characterized by a very small shear-viscosity to entropy-density ratio eta/s, near the lower bound predicted for that quantity by anti-de Sitter space/conformal field theory methods. As the produced matter expands and cools, it evolves through a phase described by a hadron gas with rapidly increasing eta/s. We calculate eta/s as a function of temperature in this phase both in and out of chemical equilibrium and find that its value poses a challenge for viscous relativistic hydrodynamics, which requires small values of eta/s in order to successfully describe the collective flow observables at the RHIC. We therefore conclude that the origin of the low viscosity matter at the RHIC must be in the partonic phase of the reaction.

Di-Jet Conical Correlations Associated with Heavy Quark Jets in anti–de Sitter Space/Conformal Field Theory Correspondence

We show that far zone Mach and diffusion wake "holograms" produced by supersonic strings in anti-de Sitter space/conformal field theory (AdS/CFT) correspondence do not lead to observable conical angular correlations in the strict N_{c}-->infinity supergravity limit if Cooper-Frye hadronization is assumed. However, a special nonequilibrium "neck" zone near the jet is shown to produce an apparent sonic boom azimuthal angle distribution that is roughly independent of the heavy quark's velocity. Our results indicate that a measurement of the dependence of the away-side correlations on the velocity of associated identified heavy quark jets at the BNL Relativistic Heavy Ion Collider and CERN LHC will provide a direct test of the nonperturbative dynamics involved in the coupling between jets and the strongly coupled quark-gluon plasma implied by AdS/CFT correspondence.

Test of the Anti–de Sitter-Space/Conformal-Field-Theory Correspondence Using High-Spin Operators

In two remarkable recent papers the planar perturbative expansion was proposed for the universal function of the coupling appearing in the dimensions of high-spin operators of the N=4 super Yang-Mills theory. We study numerically the integral equation derived by Beisert, Eden, and Staudacher, which resumes the perturbative series. In a confirmation of the anti-de Sitter-space/conformal-field-theory (AdS/CFT) correspondence, we find a smooth function whose two leading terms at strong coupling match the results obtained for the semiclassical folded string spinning in AdS5. We also make a numerical prediction for the third term in the strong coupling series.

Cutoff Anti–de Sitter Space/Conformal-Field-Theory Duality and the Quest for Braneworld Black Holes

Significant evidence is presented in favor of the holographic conjecture that "4D black holes localized on the brane found by solving the classical bulk equations in AdS5 are quantum corrected black holes and not classical ones." The quantum correction to the Newtonian potential is computed using a numerical computation of <Tab> in Schwarzschild spacetime for matter fields in the zero-temperature Boulware vacuum state. For the conformally invariant scalar field the leading order term is equivalent to that previously obtained in the weak-field approximation using Feynman diagrams and which has been shown to be equivalent, via the anti-de Sitter space/conformal-field-theory (AdS/CFT) duality, to the analogous calculation in Randall-Sundrum braneworlds. The 4D backreaction equations are used to make a prediction about the existence and the possible spacetime structure of macroscopic static braneworld black holes.