Fragile black holes and an angular momentum cutoff in peripheral heavy ion collisions

In collisions of heavy ions at extremely high energies, it is possible for a significant quantity of angular momentum to be deposited into the Quark–Gluon Plasma which is thought to be produced. We develop a simple geometric model of such a system, and show that it is dual, in the AdS/CFT sense, to a rotating AdS black hole with a topologically planar event horizon. However, when this black hole is embedded in string theory, it proves to be unstable, for all non-zero angular momenta, to a certain non-perturbative effect: the familiar planar black hole, as used in most AdS/CFT analyses of QGP physics, is “fragile”. The upshot is that the AdS/CFT duality apparently predicts that the QGP should always become unstable when it is produced in peripheral collisions. However, we argue that holography indicates that relatively low angular momenta delay the development of the instability, so that in practice it may be observable only for peripheral collisions involving favorable impact parameters, generating extremely large angular momenta. In principle, the result may be holographic prediction of a cutoff for the observable angular momenta of the QGP, or perhaps of an analogous phenomenon in condensed matter physics.     

Analytic solution for a static black hole in the RSII model

We present here a static solution for a large black hole (whose horizon radius is larger than the AdS radius) located on the brane in RSII model. According to some arguments based on the AdS/CFT conjecture, a solution for the black hole located on the brane in RSII model must encode quantum gravitational effects and therefore cannot be static. We demonstrated that a static solution can be found if the bulk is not empty. The stress energy tensor of the matter distribution in the bulk for the solution we found is physical (i.e. it is non-singular with the energy density and pressure not violating any energy conditions). The scale of the solution is given by a parameter “a”. For large values of the parameter “a” we have a limit of an almost empty AdS bulk. It is interesting that the solution cannot be transformed into the Schwarzschild-like form and does not reduce to the Schwarzschild solution on the brane. We also present two other related static solutions. At the end, we discuss why the numerical methods failed so far in finding static solutions in this context, including the solutions we found analytically here.     

Fragile black holes

The AdS/CFT correspondence may give a new way of understanding field theories in extreme conditions, as in the quark–gluon plasma phase of quark matter. The correspondence normally involves asymptotically AdS black holes with dual field theories which are defined on locally flat boundary spacetimes; the implicit assumption is that the distortions of spacetime which occur under extreme conditions do not affect the field theory in any unexpected way. However, AdS black holes are [to varying degrees] fragile, in the sense that they become unstable to stringy effects when their event horizons are sufficiently distorted. This implies that field theories on curved backgrounds may likewise be unstable in a suitable sense. We investigate this phenomenon, focussing on the “fragility” of AdS₅ black holes with flat event horizons. We find that, when they are distorted, these black holes are always unstable in string theory. This may have consequences for the detailed structure of the quark matter phase diagram at extreme values of the spacetime curvature.     

On the Conformal Side of the Penrose Limit

Motivated by the interest in understanding the role of AdS/CFT duality in the Penrose limit, whose conformal side has received so far much less attention than the corresponding string side, we construct the pp-wave limit of N=4 superconformal mechanics with the off-shell (3,4,1) multiplet. We give the superfield and the component actions, showing that the interaction part is completely fixed by symmetry. We demonstrate that for the pp-wave case the kinetic and potential terms are invariant only when taken together, as a linear combination of the two terms, provided the value of their relative coefficient is appropriately set. We explicitly show that the passing to pp-wave limit can be achieved by keeping at most quadratic nonlinearities in the action of (super)conformal mechanics.     

Lifshitz时空s波超导模型的关联长度和穿透深度

在D=d+2维各向异性的Lifshitz黑洞时空背景中, 在探子极限下, 用解析方法研究了临界温度附近引力系统的微扰, 计算出超导的关联长度ξα(1/T_c)(1-(T/T_c)^-1/2, 这与平均场论的结果一致. 进一步, 考虑在该系统中加一个均匀外磁场, 计算出穿透深度λα(T_c-T)^-1/2, 该结果与Ginzburg-Landau理论相符.     

QCD/String holographic mapping and glueball mass spectrum

Recently Polchinski and Strassler reproduced the high energy QCD scaling at fixed angles from a gauge string duality inspired by the AdS/CFT correspondence. In their approach a confining gauge theory is taken as approximately dual to an AdS space with an IR cut-off. Considering such an approximation (AdS slice) we found a one to one holographic mapping between bulk and boundary scalar fields. Associating the bulk fields with dilatons and the boundary fields with glueballs of the confining gauge theory we also found the same high energy QCD scaling. Here, using this holographic mapping, we give a simple estimate for the mass ratios of the glueballs assuming the AdS slice approximation to be valid at low energies. We also compare these results to those coming from supergravity and lattice QCD.Received: 10 September 2003, Revised: 19 November 2003, Published online: 9 January 2004     

Near-flat space limit of strings on AdS 4×ℂℙ3

The non-linear nature of string theory on non-trivial backgrounds, related to the AdS/CFT correspondence, force one to look for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit, which describes point-like strings, and the so-called “near-flat space” limit which connects two different sectors of string theory—pp-wave and “giant magnons”. Recently another example of AdS/CFT duality emerged—AdS ₄/CFT ₃, which suggests duality between CS theory and superstring theory on . In this paper we study the “near-flat space” limit of strings on an background and discuss possible applications of the limiting theory. R.C. Rashkov is on leave from Department of Physics, Sofia University, Bulgaria.     

Holographic dual of de Sitter universe with AdS bubbles

We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general d+1 spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or odd. We find that the absorption process of gravitons from the dS universe by CFT matter is controlled by localized gravitons (massive bound state modes in the Kaluza-Klein decomposition) in the dS universe. The absorption probability is determined by the effective degrees of freedom of the CFT matter and the effective gravitational coupling constant which encodes information of localized gravitons. We speculate that the dual of (d+1)-dimensional dS universe with an AdS bubble is also dual to a d-dimensional dS universe with CFT matter.     

Review of AdS/CFT Integrability,Chapter VI.1: Superconformal Symmetry

Letters in Mathematical Physics - Aspects of the D = 4, $${\mathcal N=4}$$ superconformal symmetry relevant to the AdS/CFT duality and integrability are reviewed. These include...     

Operators with Large R-Charge in N=4 Yang-Mills Theory

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong-weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well-defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions. In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two-loop level that the anomalous dimension has a finite limit when the R-charge J→∞ keeps λ/J² finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.     

Dualities and the phase diagram of the p-clock model

A new “bond-algebraic” approach to duality transformations provides a very powerful technique to analyze elementary excitations in the classical two-dimensional XY and p-clock models. By combining duality and Peierls arguments, we establish the existence of non-Abelian symmetries, the phase structure, and transitions of these models, unveil the nature of their topological excitations, and explicitly show that a continuous U(1) symmetry emerges when p?5. This latter symmetry is associated with the appearance of discrete vortices and Berezinskii-Kosterlitz-Thouless-type transitions. We derive a correlation inequality to prove that the intermediate phase, appearing for p?5, is critical (massless) with decaying power-law correlations.     

Astrobiology: a respectable new science

Holographic quantum chromodynamics (QCD) is an extra-dimensional approach to modelling hadrons, the bound states of the strong interactions. In holographic models, the extra spatial dimension creates a waveguide for fields, and the discrete towers of modes propagating in that waveguide are interpreted as hadronic resonances. These models are motivated by the AdS/CFT correspondence, which is a duality that relates theories in different numbers of spatial dimensions. Holographic models have the potential to provide a better understanding of strongly interacting systems of quarks and gluons, as well as unconventional superconductors and other nonperturbative systems.     

Aspects of holography in the AdS/CFT correspondence

We study quantities which are important for the realization of the holographic principle in the AdS/CFT correspondence: boundaries, geodesics and the propagators of scalar fields. They should play a role in the holographic setup in the BMN limit as well. We review the backgrounds and their relations that are relevant in the AdS/CFT correspondence and in its BMN limit. We describe the realization of the holographic principle in the AdS/CFT correspondence and summarize proposals of how to translate it in the BMN limit. We analyze the boundaries, geodesics and propagators of scalar fields in detail and observe how they behave in the limiting process from AdS₅×S⁵ to the 10‐dimensional plane wave, which is the spacetime in the BMN limit.     

Black hole vacua and rotation

Recent developments suggest that the near-region of rotating black holes behaves like a CFT. To understand this better, I propose to study quantum fields in this region. An instructive approach for this might be to put a large black hole in AdS and to think of the entire geometry as a toy model for the “near-region”. Quantum field theory on rotating black holes in AdS can be well-defined (unlike in flat space), if fields are quantized in the co-rotating-with-the-horizon frame. First, some generalities of constructing Hartle–Hawking Green functions in this approach are discussed. Then as a specific example where the details are easy to handle, I turn to 2+1$2+1$ dimensions (BTZ), write down the Green functions explicitly starting with the co-rotating frame, and observe some structural similarities they have with the Kerr-CFT scattering amplitudes. Finally, in BTZ, there is also an alternate construction for the Green functions: we can start from the covering AdS₃${\mathit{AdS}}_3$ space and use the method of images. Using a 19th century integral formula, I show the equality between the boundary correlators arising via the two constructions.     

Kerr black holes are not fragile

Certain AdS black holes are “fragile”, in the sense that, if they are deformed excessively, they become unstable to a fundamental non-perturbative stringy effect analogous to Schwinger pair-production [of branes]. Near-extremal topologically spherical AdS-Kerr black holes, which are natural candidates for string-theoretic models of the very rapidly rotating black holes that have actually been observed to exist, do represent a very drastic deformation of the AdS-Schwarzschild geometry. One therefore has strong reason to fear that these objects might be “fragile”, which in turn could mean that asymptotically flat rapidly rotating black holes might be fragile in string theory. Here we show that this does not happen: despite the severe deformation implied by near-extremal angular momenta, brane pair-production around topologically spherical AdS-Kerr-Newman black holes is always suppressed.     

Diquark correlations in baryon spectroscopy and holographic QCD

We improve upon recent holographic predictions for the nucleon and delta resonance spectra and show how they emerge from a straightforward extension of the “metric soft wall” AdS/QCD dual. The resulting mass formula depends on a single adjustable parameter, characterizing confinement-induced IR deformations of the anti-de Sitter metric, and on the fraction of “good” (i.e. maximally attractive) diquarks in the baryon's quark model wave function. Despite their manifest simplicity, the predicted spectra describe the masses of all 48 observed light-quark baryon states and the underlying, linear trajectory structure with unprecedented accuracy.