Higher-dimensional Anti-de Sitter Research Articles

A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)

The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operators A, B will satisfy the trace inequality Tr(AB) ≤ Tr(A)Tr(B). This relation holds on any Hilbert space H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document} and is deeply associated with the fact that the algebra B(H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}) of bounded operators on H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document} is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for Jackiw-Teitelboim gravity and we also motivate it for more general theories.

Vacuum polarization induced by a cosmic string and a brane in AdS spacetime

In this paper we investigate the vacuum polarization effects associated to a charged quantum massive scalar field on a (D+1)-dimensional anti-de Sitter background induced by a magnetic-flux-carrying cosmic string in the braneworld model context. We consider the brane parallel to the anti-de Sitter boundary and the cosmic string orthogonal to them. Moreover, we assume that the field obeys the Robin boundary condition on the brane. Because the brane divides the space into two regions with different properties of the quantum vacuum, we calculate the vacuum expectation value (VEV) of the field squared and the energy–momentum tensor (EMT) in each region. To develop these analyses, we have constructed the positive frequency Wightman function for both regions. The latter is decomposed in a part associated with the anti-de Sitter bulk in the presence of a cosmic string only, and the other part induced by the brane. The vacuum polarization effects associated with the higher-dimensional anti-de Sitter bulk in the presence of cosmic string have been developed in the literature, and here we are mainly interested in the effects induced by the brane. We show that the VEVs of the field squared and the components of the EMT induced by the cosmic string are finite on the brane. Explicitly, we compare these observables with the corresponding ones induced by the brane only, and show that near the brane the contribution induced by the latter is larger than the one induced by the string; however, for points distant from the brane the situation is reversed. Moreover, some asymptotic expressions for the VEV of the field squared and EMT are provided for specific limiting cases of the physical parameters of the model. Also, an application of our results is given for a cosmic string in the Z_2-symmetric Randall–Sundrum braneworld model with a single brane.

Holographic Van der Waals phase transition of the higher-dimensional electrically charged hairy black hole

With motivation by holography, employing black hole entropy, two-point connection function and entanglement entropy, we show that, for the higher-dimensional Anti-de Sitter charged hairy black hole in the fixed charged ensemble, a Van der Waals-like phase transition can be observed. Furthermore, based on the Maxwell equal-area construction, we check numerically the equal-area law for a first order phase transition in order to further characterize the Van der Waals-like phase transition.

Phase transition and Clapeyron equation of black holes in higher dimensional AdS spacetime

Using Maxwell's equal area law, we study the phase transition in higher dimensional anti-de Sitter (AdS) Reissner–Nordström black holes and Kerr black holes in this paper. The coexisting region of the two phases involved in the phase transition is found and some coexisting curves are shown in figures. We also analytically investigate the parameters that affect the phase transition. To better compare with a general thermodynamic system, the Clapeyron equation is derived for the higher dimensional AdS black holes.

Threefold complementary approach to holographic QCD

A complementary approach, derived from (a) higher-dimensional anti-de Sitter (AdS) space, (b) light-front quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic light-front wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group and SO(2,1). This scale appears in the light-front Hamiltonian by mapping to the evolution operator in the formalism of de Alfaro, Fubini and Furlan, which retains the conformal invariance of the action. Remarkably, the specific form of the confinement interaction and the corresponding modification of AdS space are uniquely determined in this procedure.

AdS/QCD and Applications of Light-Front Holography

Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space and frame-independent light-front wavefunctions of hadrons in (3 + 1)-dimensional physical space-time, thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD, a useful framework which describes the correspondence between theories in a modified AdS5 background and confining field theories in physical space-time. To a first semiclassical approximation, where quantum loops and quark masses are not included, this approach leads to a single-variable light-front Schrödinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role. We give an overview of the light-front holographic approach to strongly coupled QCD. In particular, we study the photon-to-meson transition form factors (TFFs) FMγ(Q2) for γ* → M using light-front holographic methods. The results for the TFFs for the η and η′ mesons are also presented. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.

Light-Front Holography, Light-Front Wavefunctions, and Novel QCD Phenomena

Light-front holography is one of the most remarkable features of the AdS/CFT correspondence. In spite of its present limitations, it provides important physical insights into the non-perturbative regime of QCD and its transition to the perturbative domain. This novel framework allows hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space to be mapped to frame-independent light-front wavefunctions of hadrons in physical space–time. The model leads to an effective confining light-front QCD Hamiltonian and a single-variable light-front Schrödinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound-state wavefunctions, and thus the fall-off as a function of the invariant mass of the constituents. The soft-wall holographic model modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics—a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryons. The model predicts a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number n. The hadron eigensolutions projected on the free Fock basis provides the complete set of valence and non-valence light-front Fock state wavefunctions \({\Psi_{n/H}(x_i, {\mathbf{k}_{\perp{i}}}, \lambda_i)}\) which describe the hadron’s momentum and spin distributions needed to compute the direct measures of hadron structure at the quark and gluon level, such as elastic and transition form factors, distribution amplitudes, structure functions, generalized parton distributions and transverse momentum distributions. The effective confining potential also creates quark–antiquark pairs from the amplitude \({q \to {q}\bar{q}{q}}\) . Thus in holographic QCD higher Fock states can have any number of extra \({q{\bar{q}}}\) pairs. We discuss the relevance of higher Fock-states for describing the detailed structure of space and time-like form factors. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann–Schwinger method in order to systematically include the QCD interaction terms. A new perspective on quark and gluon condensates is also obtained.

A new metric for rotating charged Gauss—Bonnet black holes in AdS space

In this paper, we study a new metric for slowly rotating charged Gauss-Bonnet black holes in higher-dimensional anti-de Sitter space. Taking the angular momentum parameter a up to second order, the slowly rotating charged black hole solutions are obtained by working directly in the action.

Thermodynamics of Slowly Rotating Charged Black Holes in Anti-de Sitter Einstein—Gauss—Bonnet Gravity

By using a new approach, we demonstrate the analytic expressions for slowly rotating Gauss—Bonnet charged black hole solutions with one non-vanishing angular momentum in higher-dimensional anti-de Sitter spaces. Up to linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the charged black holes get no corrections from rotation.

Fermion tunnels of higher-dimensional anti-de Sitter Schwarzschild black hole and its corrected entropy

Applying the method beyond semiclassical approximation, fermion tunneling from higher-dimensional anti-de Sitter Schwarzschild black hole is researched. In our work, the “tortoise” coordinate transformation is introduced to simplify Dirac equation, so that the equation proves that only the (r−t) sector is important to our research. Because we only need to study the (r−t) sector, the Dirac equation is decomposed into several pairs of equations spontaneously, and we then prove the components of wave functions are proportional to each other in every pair of equations. Therefore, the suitable action forms of the wave functions are obtained, and finally the correctional Hawking temperature and entropy can be determined via the method beyond semiclassical approximation.

Higher-dimensional bulk wormholes and their manifestations in brane worlds

There is nothing to prevent a higher-dimensional anti-de Sitter bulk spacetime from containing various other branes in addition to hosting our universe, presumed to be a positive-tension 3-brane. In particular, it could contain closed, microscopic branes that form the boundary surfaces of void bubbles and thus violate the null energy condition in the bulk. The possible existence of such micro branes can be investigated by considering the properties of the ground state of a pseudo-Wheeler-DeWitt equation describing brane quantum dynamics in minisuperspace. If they exist, a concentration of these micro branes could act as a fluid of exotic matter able to support macroscopic wormholes connecting otherwise distant regions of the bulk. Were the brane constituting our universe to expand into a region of the bulk containing such higher-dimensional macroscopic wormholes, they would likely manifest themselves in our brane as wormholes of normal dimensionality, whose spontaneous appearance and general dynamics would seem inexplicably peculiar. This encounter could also result in the formation of baby universes of a particular type.

New Results in Light-Front Phenomenology

The light-front quantization of gauge theories such as QCD in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and to define a kinematical definition of angular momentum. The AdS/CFT correspondence of large $N_C$ supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. I also briefly review recent analyses which shows that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.

Applications of light-front QCD

Light-front Fock state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. I also briefly review recent work which shows that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.

Black diamonds at brane junctions

We discuss the properties of black holes in brane-world scenarios where our universe is viewed as a four-dimensional sub-manifold of some higher-dimensional spacetime. We consider in detail such a model where four-dimensional spacetime lies at the junction of several domain walls in a higher dimensional anti-de Sitter spacetime. In this model there may be any number p of infinitely large extra dimensions transverse to the brane-world. We present an exact solution describing a black p-brane which will induce on the brane-world the Schwarzschild solution. This exact solution is unstable to the Gregory-Laflamme instability, whereby long-wavelength perturbations cause the extended horizon to fragment. We therefore argue that at late times a non-rotating uncharged black hole in the brane-world is described by a deformed event horizon in p+4 dimensions which will induce, to good approximation, the Schwarzschild solution in the four-dimensional brane world. When p=2, this deformed horizon resembles a black diamond and more generally for p>2, a polyhedron.