Euclidean Anti-de Sitter Research Articles

The wave function of quantum de Sitter

We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from Euclidean Anti-de Sitter space provides a natural integration contour in the space of metrics, allowing us -- with certain assumptions -- to compute the wave function exactly, including both perturbative and non-perturbative effects. The resulting wave function is a non-normalizable function of the conformal structure of future infinity which is infinitely peaked at geometries where I^+ becomes infinitely inhomogeneous. We interpret this as a non-perturbative instability of de Sitter space in three dimensional Einstein gravity.

Gravitational cusp anomalous dimension from AdS space

Recently a new picture has been developed for examining Wilson lines, and the corresponding anomalous dimensions which govern their renormalization properties. By making a particular coordinate transform, the calculation of the cusp anomalous dimension in QED or QCD can be related to the energy of a pair of static charges in Euclidean Anti-de Sitter space. This paper shows how the same picture can be used to describe Wilson lines in quantum gravity. We show how the relevant cusp anomalous dimension (which has recently been shown to be one-loop exact) can be obtained using the Newtonian limit of general relativity. We also show how both the QED and gravity cases emerge as special cases of a general formulation, and that a continuous parameter exists which interpolates between them. The results may be useful in examining the relations between gauge and gravity theories.

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functions for free massive scalar fields in $\mathbb{R}^{n}$, scalar fields in three-dimensional hyperbolic space $H_{3}$ (the Euclidean Anti-de Sitter space $AdS_{3}$), in $H_{3}/Z$ (the geometry of the Euclidean BTZ black hole), and in $S^{1}$, and the Higgs model in a $(1+1)$-dimensional finite interval. Moreover, in the above cases, we also calculate the spectra from the counting functions. Besides exact solutions, we give a general discussion on approximate solutions and construct the general series expansion for one-loop effective actions, vacuum energies, and spectral counting functions. In doing this, we encounter divergences. In order to remove the divergences, renormalization procedures are used. In this approach, these three physical quantities are regarded as spectral functions in the spectral problem.

Self-dual solutions of Yang-Mills theory on Euclidean AdS space

We find nontrivial, time-dependent solutions of the (anti) self-dual Yang-Mills equations in the four-dimensional Euclidean anti-de Sitter space. In contrast to the Euclidean flat space, the action depends on the moduli parameters and the charge can take any noninteger value.

SCALAR FIELD THEORY IN THE AdS/CFT CORRESPONDENCE: AN OPERATOR FORMULATION

Starting with a scalar field theory in Euclidean anti-de Sitter space constructed in an earlier paper, we examine the boundary limit of the quantized bulk field. Our AdS/CFT correspondence is generally valid for interacting fields, and is illustrated by a treatment of three-point function for scalar fields of arbitrary mass.

Anti-de Sitter boundary in Poincaré coordinates

We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS) space. We map the Poincare AdS boundary to the global coordinate chart and show why this boundary is not equivalent to the global AdS boundary. The Poincare AdS boundary is shown to contain points of the bulk of the entire AdS space. The Euclidean AdS space is also discussed. In this case one can define a semi-global chart that divides the AdS space in the same way as the corresponding Euclidean Poincare chart.

U(N)instantons onN=12superspace: Exact solution and geometry of moduli space

We construct the exact solution of one (anti)instanton in N=1/2 super Yang-Mills theory defined on non(anti)commutative superspace. We first identify N = 1/2 superconformal invariance as maximal spacetime symmetry. For gauge group U(2), SU(2) part of the solution is given by the standard (anti)instanton, but U(1) field strength also turns out nonzero. The solution is SO(4) rotationally symmetric. For gauge group U(N), in contrast to the U(2) case, we show that the entire U(N) part of the solution is deformed by non(anti)commutativity and fermion zero-modes. The solution is no longer rotationally symmetric; it is polarized into an axially symmetric configuration because of the underlying non(anti)commutativity. We compute the `information metric' of one (anti) instanton. We find that moduli space geometry is deformed from hyperbolic space (Euclidean anti-de Sitter space) in a way anticipated from reduced spacetime symmetry. Remarkably, the volume measure of the moduli space turns out to be independent of the non(anti)commutativity. Implications to D-branes in Ramond- Ramond flux background and Maldacena's gauge-gravity correspondence are discussed.

Information metric on instanton moduli spaces in nonlinear sigma models.

We study the information metric on instanton moduli spaces in two-dimensional nonlinear sigma models. In the CP1 model, the information metric on the moduli space of one instanton with the topological charge Q=k(k > or =1) is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti-de Sitter space-time metric in three dimensions, and the overall scale factor of the information metric is 4k(2)/3; this means that the sectional curvature is -3/4k(2). We also calculate the information metric in the CP2 model.

A holographic reduction of Minkowski space–time

Minkowski space can be sliced, outside the light-cone, in terms of Euclidean anti-de Sitter and Lorentzian de Sitter slices. In this paper we investigate what happens when we apply holography to each slice separately. This yields a dual description living on two spheres, which can be interpreted as the boundary of the light-cone. The infinite number of slices gives rise to a continuum family of operators on the two spheres for each separate bulk field. For a free field we explain how the Green's function and (trivial) S-matrix in Minkowski space can be reconstructed in terms of two-point functions of some putative conformal field theory on the two spheres. Based on this we propose a Minkowski/CFT correspondence which can also be applied to interacting fields. We comment on the interpretation of the conformal symmetry of the CFT, and on generalizations to curved space.

Exploring de Sitter space and holography

We explore aspects of the physics of de Sitter (dS) space that are relevant to holography with a positive cosmological constant. First we display a non-local map that commutes with the de Sitter isometries, transforms the bulk-boundary propagator and solutions of free wave equations in de Sitter onto the same quantities in Euclidean anti-de Sitter (EAdS), and takes the two boundaries of dS to the single EAdS boundary via an anti-podal identification. Second we compute the action of scalar fields on dS as a functional of boundary data. Third, we display a family of solutions to 3d gravity with a positive cosmological constant in which the equal time sections are arbitrary genus Riemann surfaces, and compute the action of these spaces as a functional of boundary data from the Einstein gravity and Chern–Simons gravity points of view. These studies suggest that if de Sitter space is dual to a Euclidean conformal field theory (CFT), this theory should involve two disjoint, but possibly entangled factors. We argue that these CFTs would be of a novel form, with unusual hermiticity conditions relating left movers and right movers. After exploring these conditions in a toy model, we combine our observations to propose that a holographic dual description of de Sitter space would involve a pure entangled state in a product of two of our unconventional CFTs associated with the de Sitter boundaries. This state can be constructed to preserve the de Sitter symmetries and and its decomposition in a basis appropriate to anti-podal inertial observers would lead to the thermal properties of static patch.

Notes on de Sitter space and holography

We explore aspects of the physics of de Sitter (dS) space that are relevant to holography with a positive cosmological constant. First, we display a non-local map that commutes with the de Sitter isometries, transforms the bulk–boundary propagator and solutions of free wave equations in de Sitter onto the same quantities in Euclidean anti-de Sitter (EAdS) space, and takes the two boundaries of dS to the single EAdS boundary via an antipodal identification. Second, we compute the action of scalar fields on dS as a functional of boundary data. Third, we display a family of solutions to three-dimensional gravity with a positive cosmological constant in which the equal time sections are arbitrary genus Riemann surfaces, and compute the action of these spaces as a functional of boundary data. These studies suggest that if de Sitter space is dual to a Euclidean conformal field theory (CFT), this theory should involve two disjoint, but possibly entangled factors. We argue that these CFTs would be of a novel form, with unusual hermiticity conditions relating left movers and right movers. After exploring these conditions in a toy model, we combine our observations to propose that a holographic dual description of de Sitter space would involve a pure entangled state in a product of two of our unconventional CFTs associated with the de Sitter boundaries. This state can be constructed to preserve the de Sitter symmetries and its decomposition in a basis appropriate to antipodal inertial observers would lead to the thermal properties of a static patch. To conclude, we discuss the one-parameter family of de Sitter-invariant vacua for a massive free scalar field, and their thermodynamic properties. At the free field level, we find no obvious thermodynamic reason to favour one vacuum over the other.

Scalar field theory and the definition of momentum in curvedspace

String propagation in ten-dimensionalMinkowski space or the direct product ofMinkowski space and a six-dimensionalKähler manifold or orbifold might beregarded as an approximation to a theorywhich allows for the local curvature ofspacetime by the energy-momenta of thecomponent fields. String scattering in theinteraction region might then be based onquantum field theory in a local region witha curved geometry. Special emphasis isgiven to field theory in anti-de Sitterspace, as it represents a maximallysymmetric spacetime of constant curvaturewhich could arise in the description ofmatter interactions in local regions ofspacetime. Curvature shifts in themomentum and squared mass are evaluatedfor scalar fields in anti-de Sitter space,and it is shown that the shift in p2 + m2 compensates the ground-statecontribution to the bosonic stringHamiltonian, implying the consistency ofcomputing the scattering entirely in flatspace. Dual space rules for evaluatingFeynman diagrams in Euclideananti-de Sitter space are initially definedusing eigenfunctions based on generalizedplane waves. Loop integrals can beevaluated even more easily using momentumspace rules in conformally flatcoordinates for anti-de Sitter space,which admits flat three-dimensionalsections that are analytic continuationsof horospheres in hyperbolic space H4.An additional argument in favour of themodel of string propagation described inthis paper is based on the removal ofreflective boundary conditions on quantumfields interacting in a locallyanti-de Sitter region without spatialinfinity, implying the existence of aone-parameter family of O(3,2)-invariantvacua in this region consistent with thedegree of freedom in defining the stringtheory vacuum.

Spinor exchange in AdS d+1

We explicitly calculate a Witten diagram with general spinor field exchange on ( d+1)-dimensional Euclidean Anti-de Sitter space, which is necessary to evaluate four-point correlation functions with spinor fields when we make use of the AdS/CFT correspondence, especially in supersymmetric cases. We also show that the amplitude can be reduced to a scalar exchange amplitude. We discuss the operator product expansion of the dual conformal field theory by interpreting the short distance expansion of the amplitude according to the AdS/CFT correspondence.

Evidence for large N phase transition in Script N = 4 super Yang-Mills theory at finite temperature

The AdS/CFT correspondence provides valuable constraints on the possible exact form of various physical quantities in the ${\cal N}=4$ super Yang-Mills theory in the large N limit. We examine the free energy as the expansions in a small as well as in a large 't Hooft parameter $\lambda$. We argue that it is impossible to smoothly extrapolate from the weak coupling regime to the strong coupling regime, thus there must exist a large N phase transition in $\lambda$ at a finite temperature. We also argue that there is no world-sheet instanton in the background of the Euclidean anti-de Sitter black hole.

Spinors and the AdS/CFT correspondence

We consider a free massive spinor field in Euclidean Anti-de Sitter space. The usual Dirac action in bulk is supplemented by a certain boundary term. The boundary conditions of the field are parametrized by a spinor on the boundary, subject to a projection. We calculate the dependence of the partition function on this boundary spinor. The result agrees with the generating functional of the correlation functions of a quasi-primary spinor operator, of a certain scaling dimension, in a free conformal field theory on the boundary.

Euclidean superconformal symmetry and its relation with minkowski supersymmetries

We write down the extended D = 4 euclidean superconformal algebra SL(2, N; H) in quaternionic as well as complex notation. Only for even N the analytic continuation of the Minkowski conformal supersymmetry SU(2, 2; N) to the D = 4 euclidean conformal supersymmetry does exist. The (noncompact) euclidean internal symmetry group is U*(2N). The euclidean anti de Sitter and de Sitter extended supersymmetries are discussed also.