We present geometric derivations of the Smarr formula for static AdS black holes and an expanded first law that includes variations in the cosmological constant. These two results are further related by a scaling argument based on Euler's theorem. The key new ingredient in the constructions is a two-form potential for the static Killing field. Surface integrals of the Killing potential determine the coefficient of the variation of Λ in the first law. This coefficient is proportional to a finite, effective volume for the region outside the AdS black hole horizon, which can also be interpreted as minus the volume excluded from a spatial slice by the black hole horizon. This effective volume also contributes to the Smarr formula. Since Λ is naturally thought of as a pressure, the new term in the first law has the form of effective volume times change in pressure that arises in the variation of the enthalpy in classical thermodynamics. This and related arguments suggest that the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime.

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Enthalpy and the mechanics of AdS black holes

The contents of this review reflect some of the shifts of emphasis that are occurring among the fields of astrophysics, nuclear physics, and elementary particle physics. Particle physics has made great advances in the unification of the fundamental forces of nature. Discussions and planning for a next big step in accelerator-colliders are presented. The technology of superconducting magnet systems as well as the fundamental physical principles of particle accelerators are discussed. Also presented are: high-resolution electronic particle detectors; nuclear physics changes such as pion interactions within nuclei; discussion of future relativistic heavy-ion colliders; the role of rotational degrees of freedom in heavy-ion collisions at low and moderate energies; hyperon beta decays; and the analysis of materials via nuclear reaction techniques. Neutrinos, their interactions and possible masses, have an important bearing on cosmology and the matter density of the universe in addition to their inherent interest in the microscopic world and this is also examined.

Annual Review of Nuclear and Particle Science

We review recent progress in studying mesons within gauge/gravity duality, in the context of adding flavour degrees of freedom to generalizations of the AdS/CFT correspondence. Our main focus is on the “top-down approach” of considering models constructed within string theory. We explain the string-theoretical constructions in detail, aiming at non-specialists. These give rise to a new way of describing strongly coupled confining large-N gauge theories similar to large-N QCD. In particular, we consider gravity dual descriptions of spontaneous chiral symmetry breaking, and compare with lattice results. A further topic covered is the behaviour of flavour bound states in finite-temperature field theories dual to a gravity background involving a black hole. We also describe the “bottom up” phenomenological approach to mesons within AdS/QCD. Some previously unpublished results are also included.

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Mesons in gauge/gravity duals

In this thesis we consider certain supersymmetric string theories on curved backgrounds containing the three-dimensional anti-de Sitter space, AdS3. On the one hand, these are gravity theories in three dimensions, which makes them simpler than real-world gravity but still rich in interesting phenomena. On the other hand, according to the holographic duality, each of these gravitational theories should be equivalent to a suitable quantum field theory with conformal symmetry in two dimensions, a CFT2. In that low dimension, such conformal field theories enjoy an infinite-dimensional Virasoro symmetry which strongly constrains them, but remain non-trivial. Our study is confined to a particular regime, the 't Hooft limit, in which the strings propagate freely. Free string theory can be described as a non-linear sigma model from the string worldsheet (geometrically, a two-dimensional cylinder) into a target space of the form AdS3xM, where M is a manifold without boundary. For us, M is a product of circles and three-dimensional spheres, namely M=S3xT4 or M=S3xS3xS1, both of which enjoy 16 supersymmetries. For the sake of brevity, our presentation is mostly focused on the massive sector of the former geometry, while more general cases are discussed in the concluding chapter. Our main result is to describe how these theories are integrable at the quantum level, i.e. how their worldsheet scattering matrix factorises and their spectrum can be efficiently computed by Bethe ansatz techniques. This is done both from the point of view of the worldsheet theory and of a dual spin chain picture. We also discuss how this procedure is supported by overwhelming evidence from independent (perturbative or semiclassical) calculations, up to two loops in the worldsheet theory expansion.

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Towards integrability for AdS3/CFT2

We analyze the phases of the Sakai-Sugimoto model at finite temperature and baryon chemical potential. Baryonic matter is represented either by 4-branes in the 8-branes or by strings stretched from the 8-branes to the horizon. We find the explicit configurations and use them to determine the phase diagram and equation of state of the model. The 4-brane configuration (nuclear matter) is always preferred to the string configuration (quark matter), and the latter is also unstable to density fluctuations. In the deconfined phase the phase diagram has three regions corresponding to the vacuum, quark-gluon plasma, and nuclear matter, with a first-order and a second-order phase transition separating the phases. We find that for a large baryon number density, and at low temperatures, the dominant phase has broken chiral symmetry. This is in qualitative agreement with studies of QCD at high density.

Holographic Nuclear Physics

In the framework of a holographic QCD approach we study the influence of matter on the deconfinement temperature T{sub c}. We first consider the quark flavor number (N{sub f}) dependence of T{sub c}. We observe that T{sub c} decreases with N{sub f}, which is consistent with a lattice QCD result. We also delve into how the quark number density {rho}{sub q} affects the value of T{sub c}. We find that T{sub c} drops with increasing {rho}{sub q}. In both cases, we confirm that the contributions from quarks are suppressed by 1/N{sub c}, as it should be, compared to the ones from a gravitational action (pure Yang-Mills theory)

Deconfinement phase transition in holographic QCD with matter

Encouraged by recent developments in AdS/QCD models for the light quark system, we study heavy quarkonium in the framework of the AdS/QCD models. We calculate the masses of $c\overline{c}$ vector meson states using the AdS/QCD models at zero and at finite temperature. Among the models adopted in this work, we find that the soft-wall model describes the low-lying heavy quark meson states at zero temperature relatively well. At finite temperature, we observe that once the bound state is above ${T}_{c}$, its mass will increase with temperature until it dissociates at a temperature of around 494 MeV. It is shown that the dissociation temperature is fixed by the infrared cutoff of the models. The present model serves as a unified nonperturbative model to investigate the properties of bound quarkonium states above ${T}_{c}$.

Heavy quarkonium in a holographic QCD model

We study the physics at finite nuclear density in the framework of the AdS/QCD model with a holographic baryon field included. Based on a mean field type approach, we introduce the nucleon density as a bi-fermion condensate of the lowest mode of the baryon field and calculate the density dependence of the chiral condensate and the nucleon mass. We observe that the chiral condensate as well as the mass of nucleon decrease with increasing nuclear density. The resulting density dependence is, however, much weaker than those obtained in earlier studies based on other QCD effective theories. We also consider the mass splitting of charged vector mesons in isospin asymmetric nuclear matter.

Holographic nuclear matter in the AdS/QCD model

We compute the potential between a pair of nucleons in the D4-D8 holographic QCD. In the large 't Hooft coupling limit, λ >> 1, the hadronic size of the baryon is small ~ 1/λ1/2MKK, and their interaction with mesons are well approximated by a set of dimension four and five operators. The nucleon-nucleon potential emerges from one-boson exchange picture involving massless pseudo-scalars and an infinite tower of spin one mesons. We find in particular that ρ meson exchanges are dominated by a dimension five derivative coupling of tensor type, whereas for ω mesons and axial mesons, such tensor couplings are completely absent. The potential is universally repulsive ~ 1/r2 at short distance, and has the usual long-distance attractive behavior ~ −1/r3 along a isosinglet and spin triplet channel. Both the large Nc form and the finite Nc form are given. In the former, a shallow classical minimum of depth ~ 0.1MKKNc/λ forms at around rMKK 5.5.

Holographic Deuteron and Nucleon-Nucleon Potential

We compute the potential between a pair of nucleons in the D4-D8 holographic QCD. In the large 't Hooft coupling limit, $\lambda \gg 1$, the hadronic size of the baryon is small $\sim 1/\sqrt{\lambda}M_{KK}$, and their interaction with mesons are well approximated by a set of dimension four and five operators. The nucleon-nucleon potential emerges from one-boson exchange picture involving massless pseudo-scalars and an infinite tower of spin one mesons. We find in particular that $\rho$ meson exchanges are dominated by a dimension five derivative coupling of tensor type, whereas for $\omega$ mesons and axial mesons, such tensor couplings are completely absent. The potential is universally repulsive $\sim 1/r^2$ at short distance, and has the usual long-distance attractive behavior $\sim -1/r^3$ along a isosinglet and spin triplet channel. Both the large $N_c$ form and the finite $N_c$ form are given. In the former, a shallow classical minimum of depth $\sim 0.1M_{KK}{N_c/\lambda}$ forms at around $rM_{KK}\simeq 5.5$.

Youngman Kim

Papers

Deconfinement phase transition in holographic QCD with matter

Heavy quarkonium in a holographic QCD model

Holographic nuclear matter in the AdS/QCD model

Holographic Deuteron and Nucleon-Nucleon Potential

Holographic Deuteron and Nucleon-Nucleon Potential