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Search Results: 1 - 10 of 18683 matches for " Alberto Enciso "
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Spin models of Calogero-Sutherland type and associated spin chains
Alberto Enciso
Physics , 2009,
Abstract: Several topics related to quantum spin models of Calogero-Sutherland type, partially solvable spin chains and Polychronakos's "freezing trick" are rigorously studied.
Spinor Green's functions via spherical means on products of space forms
Alberto Enciso,Niky Kamran
Physics , 2010, DOI: 10.1016/j.geomphys.2010.09.021
Abstract: We explicitly compute the Green's function of the spinor Klein-Gordon equation on the Riemannian and Lorentzian manifolds of the form $M_0 \times ... \times M_N$, with each factor being a space of constant sectional curvature. Our approach is based on an extension of the method of spherical means to the case of spinor fields and on the use of Riesz distributions.
Global causal propagator for the Klein-Gordon equation on a class of supersymmetric AdS backgrounds
Alberto Enciso,Niky Kamran
Physics , 2010,
Abstract: We analyze the Cauchy problem for the Klein-Gordon equation on the type IIB supergravity backgrounds $AdS^5 \times Y^{p,q}$, where $Y^{p,q}$ is any of the Sasaki-Einstein 5-manifolds recently discovered by Gaunlett, Martelli, Sparks and Waldram (Adv. Theor. Math. Phys. 8 (2004) 711--734). Although these spaces are not globally hyperbolic, we prove that there exists a unique admissible propagator and derive an integral representation thereof using spectral-theoretic techniques.
Causality and the conformal boundary of AdS in real-time holography
Alberto Enciso,Niky Kamran
Physics , 2012, DOI: 10.1103/PhysRevD.85.106016
Abstract: We consider the holographic prescription problem in a (Lorentzian) AdS background, deriving from first principles the explicit formulas that relate the field at infinity with the field in the bulk. In contrast with the previous studies of the "real-time" holography problem, our derivation uses purely classical arguments that involve causality, as in the usual treatment of the holographic prescription problem in Wick-rotated spaces of Euclidean signature. We show that there is a unique propagator that preserves causality and see that this provides a simple picture of the relationship between the bulk manifold and its conformal boundary.
Determining an asymptotically AdS spacetime from data on its conformal boundary
Alberto Enciso,Niky Kamran
Physics , 2015, DOI: 10.1007/s10714-015-1974-5
Abstract: An outstanding question lying at the core of the AdS/CFT correspondence in string theory is the holographic prescription problem for Einstein metrics, which asserts that one can slightly perturb the conformal geometry at infinity of the anti-de Sitter space and still obtain an asymptotically anti-de Sitter spacetime that satisfies the Einstein equations with a negative cosmological constant. The purpose of this paper is to address this question by providing a precise quantitative statement of the real-time holographic principle for Einstein spacetimes, to outline its proof and to discuss its physical implications.
Green's function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces
Alberto Enciso,Niky Kamran
Mathematics , 2008, DOI: 10.1007/s00220-009-0826-0
Abstract: We compute the Green's function for the Hodge Laplacian on the symmetric spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and \Sigma is a simply connected Riemannian surface of constant curvature. Our approach is based on a generalization to the case of differential forms of the method of spherical means and on the use of Riesz distributions on manifolds. The radial part of the Green's function is governed by a fourth order analogue of the Heun equation.
A singular initial-boundary value problem for nonlinear wave equations and holography in asymptotically anti-de Sitter spaces
Alberto Enciso,Niky Kamran
Mathematics , 2013,
Abstract: We analyze the initial value problem for semilinear wave equations on asymptotically anti-de Sitter spaces using energy methods adapted to the geometry of the problem at infinity. The key feature is that the coefficients become strongly singular at infinity, which leads to considering nontrivial data on the conformal boundary of the manifold. This question arises in Physics as the holographic prescription problem in string theory.
Lorentzian Einstein metrics with prescribed conformal infinity
Alberto Enciso,Niky Kamran
Mathematics , 2014,
Abstract: We prove that there are asymptotically anti-de Sitter Einstein metrics with prescribed conformal infinity. More precisely we show that, given any suitably small perturbation $\hat g$ of the conformal metric of the $(n+1)$-dimensional anti-de Sitter space at timelike infinity, which is given by the canonical Lorentzian metric on the $n$-dimensional cylinder, there is a Lorentzian Einstein metric on $(-T,T)\times \mathbb{B}^n$ whose conformal geometry is given by $\hat g$. This is a Lorentzian counterpart of the Graham-Lee theorem in Riemannian geometry and is motivated by the holographic prescription problem in the context of the AdS/CFT correspondence in string theory.
The fermion density operator in the droplet bosonization picture
Alberto Enciso,Alexios P. Polychronakos
Mathematics , 2006, DOI: 10.1016/j.nuclphysb.2006.06.014
Abstract: We derive the phase space particle density operator in the 'droplet' picture of bosonization in terms of the boundary operator. We demonstrate that it satisfies the correct algebra and acts on the proper Hilbert space describing the underlying fermion system, and therefore it can be used to bosonize any hamiltonian or related operator. As a demonstration we show that it reproduces the correct excitation energies for a system of free fermions with arbitrary dispersion relations.
Submanifolds that are level sets of solutions to a second-order elliptic PDE
Alberto Enciso,Daniel Peralta-Salas
Mathematics , 2010,
Abstract: Motivated by a question of Rubel, we consider the problem of characterizing which noncompact hypersurfaces in $\RR^n$ can be regular level sets of a harmonic function modulo a $C^\infty$ diffeomorphism, as well as certain generalizations to other PDEs. We prove a versatile sufficient condition that shows, in particular, that any (possibly disconnected) algebraic noncompact hypersurface can be transformed onto a union of components of the zero set of a harmonic function via a diffeomorphism of $\RR^n$. The technique we use, which is a significant improvement of the basic strategy we recently applied to construct solutions to the Euler equation with knotted stream lines (Ann. of Math., in press), combines robust but not explicit local constructions with appropriate global approximation theorems. In view of applications to a problem of Berry and Dennis, intersections of level sets are also studied.
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