Hagedorn states and thermalization

In recent years Hagedorn states have been used to explain the physics close to the critical temperature within a hadron gas. Because of their large decay widths these massive resonances lower η/s to near the AdS/CFT limit within the hadron gas phase. A comparison of the Hagedorn model to recent lattice results is made and it is found that for both T _c = 176 MeV and T _c = 196 MeV, the hadrons can reach chemical equilibrium almost immediately, well before the chemical freeze-out temperatures found in thermal fits for a hadron gas without Hagedorn states. In this paper we also observe the effects of Hagedorn States on the K ⁺/π⁺ horn seen at AGS, SPS, and RHIC.     

Transport properties of the fluid produced at relativistic heavy-ion collider

It is by now well known that the relativistic heavy-ion collisions at RHIC, BNL have produced a strongly interacting fluid with remarkable properties, among them the lowest ever observed ratio of the coefficient of shear viscosity to entropy density. Arguments based on ideas from the string theory, in particular the AdS/CFT correspondence, led to the conjecture — now known to be violated — that there is an absolute lower limit 1/4π on the value of this ratio. Causal viscous hydrodynamics calculations together with the RHIC data have put an upper limit on this ratio, a small multiple of 1/4π, in the relevant temperature regime. Less well-determined is the ratio of the coefficient of bulk viscosity to entropy density. These transport coefficients have also been studied non-perturbatively in the lattice QCD framework, and perturbatively in the limit of high-temperature QCD. Another interesting transport coefficient is the coefficient of diffusion which is also being studied in this context. In this paper some of these recent developments are reviewed and then the opportunities presented by the anticipated LHC data are discussed, for the general nuclear physics audience.     

Entanglement entropy and gravity/condensed matter correspondence

The entanglement entropy has been very important in various subjects such as the quantum information theory, condensed matter physics and quantum gravity. Especially, for more than twenty years, this quantity has been studied by many people in order to obtain a quantum mechanical interpretation of the gravitational entropy such as the black hole entropy. We will introduce recent progresses toward this long-standing problem in quantum gravity by applying the idea of holography, especially the AdS/CFT correspondence found in string theory. We will explain the holographic formula which computes the entanglement entropy of quantum field theories in terms of the area of minimal surfaces in general relativity. We will also review the recent application of AdS/CFT correspondence to condensed matter physics from the viewpoint of entanglement entropy.     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.     

The Classical <Emphasis Type="Italic">R</Emphasis>-Matrix of AdS/CFT and its Lie Dialgebra Structure

The classical integrable structure of \mathbbZ₄{\mathbb{Z}_4}-graded supercoset σ-models, arising in the AdS/CFT correspondence, is formulated within the R-matrix approach. The central object in this construction is the standard R-matrix of the \mathbbZ₄{\mathbb{Z}_4}-twisted loop algebra. However, in order to correctly describe the Lax matrix within this formalism, the standard inner product on this twisted loop algebra requires a further twist induced by the Zhukovsky map, which also plays a key role in the AdS/CFT correspondence. The non-ultralocality of the σ-model can be understood as stemming from this latter twist since it leads to a non-skew-symmetric R-matrix.     

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.     

A uniqueness theorem for the anti-de Sitter soliton

The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons, this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the anti-de Sitter (AdS) soliton, a globally static, asymptotically toroidal Lambda<0 spacetime with negative mass. Nonetheless, arguing from the AdS conformal field theory (AdS/CFT) correspondence, Horowitz and Myers proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static Lambda<0 spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.     

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.     

Axiomatic Conformal Theory in Dimensions &gt;2 and AdS/CT Correspondence

We formulate axioms of conformal theory (CT) in dimensions >2 modifying Segal’s axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT, one includes also a condition of existence of energy-momentum tensor.) We use these axioms to derive the AdS/CT correspondence for local theories on AdS. We introduce a notion of weakly local quantum field theory and construct a bijective correspondence between conformal theories on the sphere S^d and weakly local quantum field theories on \({H^{d+1}}\) that are invariant with respect to isometries. (Here \({H^{d+1}}\) denotes hyperbolic space = Euclidean AdS space.) We give an expression of AdS correlation functions in terms of CT correlation functions. The conformal theory has conserved energy-momentum tensor iff the AdS theory has graviton in its spectrum.     

Black holes,AdS, and CFTs

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein–Hawking entropy S _BH is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly while there is a valid context in which this result can be restated as “S _BH counts all states inside the black hole,” there may also be another in which it may be restated as “S _BH does not count all states inside the black hole, but only those that are distinguishable from the outside.” The arguments and conclusions represent the author’s translation of the community’s collective wisdom, combined with a few recent results.     

A Stress Tensor for Anti-de Sitter Gravity

We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS₅, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S ³×R. Received: 20 April 1999 / Accepted: 8 July 1999     

Holographic Entanglement Entropy of the BTZ Black Hole

We investigate quantum entanglement of gravitational configurations in 3D AdS gravity using the AdS/CFT correspondence. We derive explicit formulas for the holographic entanglement entropy (EE) of the BTZ black hole, conical singularities and regularized AdS₃. The leading term in the large temperature expansion of the holographic EE of the BTZ black hole reproduces exactly its Bekenstein-Hawking entropy S _BH , whereas the subleading term behaves as ln S _BH . We also show that the leading term of the holographic EE for the BTZ black hole can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. This result indicates that black hole EE is not a fundamental feature of the underlying theory of quantum gravity but emerges when the semiclassical notion of spacetime geometry is used to describe the black hole.     

Extracting hadronic viscosity from microscopic transport models

Ultrarelativistic heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC) are thought to have created a Quark–Gluon Plasma, characterized by a very small shear viscosity to entropy density ratio η/s, close to the lower bound predicted for that quantity by string theory. However, due to the dynamics of the collision, the produced matter passes through a phase characterized by an expanding and rapidly cooling hadron gas with strongly increasing η/s. Such a rise in η/s would not be compatible with the success of (viscous) hydrodynamics, which requires a very small value of η/s throughout the full evolution of the reaction in order to successfully describe the collective flow seen in the experiments. Here we show that the inclusion of a pion-chemical potential, which is bound to arise due to the separation of chemical and kinetic freeze-out during the collision evolution, will reduce the value of η/s, and argue that introduction of other chemical potentials could ensure the successful application of (viscous) hydrodynamics to collisions at RHIC.     

Hadronic η and $ \eta{^\prime}$ decays

The hadronic decays η, ↦3π and ↦ηππ are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving s- and p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. Very good overall agreement with currently available data on decay widths and spectral shapes is achieved.     

Strong decays B<Subscript>s0</Subscript>→B<Subscript>s</Subscript>π and B<Subscript>s1</Subscript>→B<Superscript>*</Superscript><Subscript>s</Subscript>π with light-cone QCD sum rules

In this article, we calculate the strong coupling constants g_Bs0Bsη and g_Bs1B*sη with the light-cone QCD sum rules. Then we take into account the small η–π⁰ transition matrix according to Dashen’s theorem, and we obtain the small decay widths for the isospin violation processes B_s0→B_sη→B_sπ⁰ and B_s1→B_s ^*η→B_s ^*π⁰. We can search the strange-bottomed (0⁺,1⁺) mesons B_s0 and B_s1 in the invariant B_sπ⁰ and B^* _sπ⁰ mass distributions, respectively. PACS  12.38.Lg; 13.25.Hw; 14.40.Nd     

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.     

The cusp effect in <Emphasis Type="Italic">η</Emphasis>′→<Emphasis Type="Italic">η</Emphasis><Emphasis Type="Italic">π</Emphasis><Emphasis Type="Italic">π</Emphasis> decays

Strong final-state interactions create a pronounced cusp in η′→η π ⁰ π ⁰ decays. We adapt and generalize the non-relativistic effective field theory framework developed for the extraction of π π scattering lengths from K→3π decays to this case. The cusp effect is predicted to have an effect of more than 8% on the decay spectrum below the π ⁺ π ⁻ threshold.