arXiv subjects
Publications and source records attributed to Enrique Alvarez.
The so called unimodular theory of gravitation is compared with general relativity in the quadratic (Fierz-Pauli) regime, using a quite broad framework, and it is argued that quantum effects allow in principle to discriminate between both theories.
The obstruction for a perturbative reconstruction of the five-dimensional bulk metric starting from the four-dimensional metric at the boundary,that is, the Dirichlet problem, is computed in dimensions $6\leq d\leq 10$ and some comments are made on its general structure and, in particular, on its relationship with the conformal anomaly, which we compute in dimension $d=8$.
The whole idea of holography as put forward by Gerard 't Hooft assumes that data on a boundary determine physics in the volume. This corresponds to a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) problem in the lorentzian setting. Is this last aspect of the problem that is explored here for Ricci flat spaces with vanishing cosmological constant.
Some kinematical speculations on the infinite curvature limit of the conjectured duality of Maldacena between ten-dimensional strings living in $AdS_5\times S_5$ and a ordinary four-dimensional quantum field theory, namely ${\cal{N}}=4$ super Yang-Mills with gauge group SU(N) are given.
An elementary introduction to Maldacena's AdS/CFT correspondence is given, with some emphasis in the Fefferman-Graham construction. This is based on lectures given by one of us (E.A.) at the Universidad Autonoma de Madrid.
A holographic interpretation for some specific Ricci flat string backgrounds of the form $A_6\times C_4$ is proposed. The conjecture is that there is a Four-dimensional Euclidean Conformal Field Theory (ECFT) defined on a codimension two {\em submanifold} of the manifold $A_6$ (where one of the two remaining {\em holographic} coordinates of $A_6$ is timelike, and the other one spacelike), with central charge proportional to the radius of curvature of the six-dimensional manifold, $c\sim l^4$.
This paper has been superseded by hep-th/0303164, "The Dirichlet Obstruction in AdS/CFT"
The static potential, corresponding to the interaction of two heavy sources is computed for $\mathcal{N}=4$ Super Yang Mills in the strong 't Hooft coupling regime by using the AdS/CFT conjecture and performing a computation of a rectangular Wilson loop at a finite distance of the boundary.
The low energy physics as predicted by strings can be expressed in two (conformally related) different variables, usually called {\em frames}. The problem is raised as to whether it is physically possible in some situations to tell one from the other.
$AdS_{5}$ with linear dilaton and non vanishing $B$-field is shown to be a solution of the non critical string beta function equations. A non critical $(D=5)$ solution interpolating between flat space-time and $AdS_{5}$, with asymptotic linear dilaton and non vanishing $B$-field is also presented. This solution is free of space-time singularities and has got the string coupling constant everywhere bounded. Both solutions admit holographic interpretation in terms of ${\cal N}=0$ field theories. Closed string tachyon stability is also discussed.
The static gauge potential between heavy sources is computed from a recently introduced non-critical bosonic string background. When the sources are located at the infinity of the holographic coordinate, the linear dilaton behavior is recovered, which means that the potential is exactly linear in the separation between the sources. When the sources are moved towards the origin, a competing overconfining cubic branch appears, which is however disfavored energetically.
Sigma model ($α^{\prime}$) corrections to the confining string background are obtained. The main result is that the Poincaré invariant ansatz is maintained. Physical conditions for the dissapearance of the naked singularity are discussed.
A non supersymmetric string background, directly derived from the string soft dilaton theorem, is used to compute, in the semiclassical approximation, the expectation value of Wilson loops in static gauge. The resulting potential shares common features with the one obtained through Schwarzschild-anti de Sitter spacetime metrics. In particular a linear confining potential appears naturally.
A string background, which is in some precise sense {\em universal} (i.e., incorporating all orders in the Feynman diagram expansion), is proposed to represent pure gauge theories. S-duality at the level of the string metric is considered as well as the vacuum expectation values of 't Hooft and Wilson loops in semiclassical approximation.
The equivalence between the holographic renormalization group and the soft dilaton theorem is shown for a class of wrapped metrics solutions of the string beta function equations for the bosonic string.
The renormalization group approach towards the string representation of non abelian gauge theories translates, in terms of the string sigma model beta function equations, the renormalization group evolution of the gauge coupling constant and Zamolodchikov`s $c$ function. Tachyon stability, glueball mass gap, renormalization group evolution of the $c$ function and the area law for the Wilson loop are studied for a critical bosonic string vacuum corresponding to a non abelian gauge theory in four dimensional space-time. We prove that the same intrinsic geometry for the string vacuum is universal in some sense, reproducing the Yang-Mills beta function to arbitrary loop order in perturbation theory.
The infinite tension limit of string amplitudes is examined with some care, identifying the part responsible of diamagnetic behaviour as well as a peculiar paramagnetic {\em tachyon magnifying} responsible of asymptotic freedom. The way string theory represents abelian gauge theories is connected with the non-planar reggeon/pomeron amplitude and a nontrivial beta function is found in the low energy limit of a single D-brane.