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Orlando Alvarez

Publications and source records attributed to Orlando Alvarez.

At least 19 recordsLinked to original sources
arXiv2019

Perturbations to Generalized Kink-like Topological Defects in $AdS$

We explore perturbations to a kink-like (codimension 1) topological defect whose world brane is $AdS_{q}$ embedded into $AdS_{q+1}$. Previously, we found solutions in the limit the mass of the scalar field vanishes. In this article we extend a calculation previously done in $AdS_{2}$ to higher-dimensional embedding spaces and find that all perturbations to the mass of the field are stable to first order as expected in a theory with topological defects. We find that the equation of motion to the correction strongly resembles a problem well-known in quantum mechanics.

hep-th↗
arXiv2019

Perturbations to Kink-Like Topological Defects in 2D Anti de Sitter Spacetime

We examine codimension--1 topological defects whose associated worldline is geodesically embedded in $\AdS_{2}$. This discussion extends a previous study of exact analytical solutions to the equations of motion of topological defects in $\AdS_{n}$ in a particular limit where the masses of the scalar and gauge field vanish. We study the linear perturbations about the zeroth order kink-like solution and verify that they are stable. We also discuss general features of the perturbation expansion to all orders.

hep-th↗
arXiv2018

Some Exact Solutions for Maximally Symmetric Topological Defects in Anti de Sitter Space

We obtain exact analytical solutions for a class of SO($l$) Higgs field theories in a non-dynamic background $n$-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric $p$-dimensional topological defects where $n=(p+1)+l$. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both $p$ and $l$. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ($p=0,1,2,\dotsc;\, l=1$), vortex-like defects ($p=1,2,3;\, l=2$), and the 'tHooft-Polyakov monopole ($p=0;\, l=3$). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

hep-th↗
arXiv2017

Emergent Gravity in Spaces of Constant Curvature

In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical method requires a generalization of a formula due to by Hermann Weyl. While the first paper discussed the framework in Euclidean (Minkowski) space, here we discuss how this framework generalizes to spaces of constant sectional curvature. We focus primarily on anti de Sitter space. We then discuss how such a theory can give rise to a cosmological constant and Planck mass that are within reasonable bounds of the experimental values.

hep-th↗
arXiv2017

Emergent Gravity and Weyl's Volume Formula

In physical theories where the energy (action) is localized near a submanifold of Euclidean (Minkowski) space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This universal expression is a generalization of an exact formula of Hermann Weyl for the volume of a tube. We describe when our result is applicable, when our generalization gives an exact result, and when there are corrections (often exponentially small) to our formula. In special situations, dictated by spherical symmetry, the expression is a generalized Lovelock lagrangian for gravity, a class of theories that are interesting because they have no negative metric states. We discuss whether these results represent a true theory of emergent gravity by discussing simple models where a higher dimensional quantum field theory without a fundamental graviton leads to a gravity-like theory on a submanifold where all or some of the dynamical degrees of freedom are fluctuations of the metric on the submanifold.

hep-th↗
arXiv2011

Beyond the String Genus

In an earlier work we used a path integral analysis to propose a higher genus generalization of the elliptic genus. We found a cobordism invariant parametrized by Teichmuller space. Here we simplify the formula and study the behavior of our invariant under the action of the mapping class group of the Riemann surface. We find that our invariant is a modular function with multiplier just as in genus one.

hep-th↗
arXiv2009

Schwarzschild Spacetime without Coordinates

We discuss how to construct the full Schwarzschild (Kruskal-Szekeres) spacetime in one swoop by using the bundle of orthonormal Lorentz frames and the Einstein equation without the use of coordinates. We never have to write down the Kruskal-Szekeres or an equivalent form of the metric.

gr-qc↗
arXiv2009

Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.

hep-th↗
arXiv2007

Target Space Duality: The Dilaton Field

Classical target space duality transformations are studied for the non-linear sigma model with a dilaton field. Working within the framework of the Hamiltonian formalism we require the duality transformation to be a property only of the target spaces. We obtain a set of restrictions on the geometrical data.

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arXiv2007

Target Space Duality III: Potentials

We generalize previous results on target space duality to the case where there are background fields and the sigma model lagrangian has a potential function.

hep-th↗
arXiv2002

Pseudoduality in Sigma Models

We revisit classical "on shell" duality, i.e., pseudoduality, in two dimensional conformally invariant classical sigma models and find some new interesting results. We show that any two sigma models that are "on shell" duals have opposite 1-loop renormalization group beta functions because of the integrability conditions for the pseudoduality transformation. A new result states for any two compact Lie groups of the same dimension there is a natural pseudoduality transformation that maps classical solutions of the WZW model on the first group into solutions of the WZW model on the second group. This transformation preserves the stress-energy tensor. The two groups can be non-isomorphic such as B_n and C_n in the Cartan notation. This transformation can be used for a new construction of non-local conserved currents. The new non-local currents on G depend on the choice of dual group G-tilde.

hep-th↗
arXiv2001

Beyond the Elliptic Genus

Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.

hep-th↗
arXiv2000

Target Space Pseudoduality Between Dual Symmetric Spaces

A set of on shell duality equations is proposed that leads to a map between strings moving on symmetric spaces with opposite curvatures. The transformation maps "waves" on a riemannian symmetric space to "waves" on its dual riemannian symmetric space. This transformation preserves the energy momentum tensor though it is not a canonical transformation. The preservation of the energy momentum tensor has a natural geometrical interpretation. The transformation maps "particle-like solutions" into static "soliton-like solutions". The results presented here generalize earlier results of E. Ivanov.

hep-th↗
arXiv2000

Target Space Duality II: Applications

We apply the framework developed in Target Space Duality I: General Theory. We show that both nonabelian duality and Poisson-Lie duality are examples of the general theory. We propose how the formalism leads to a systematic study of duality by studying few scenarios that lead to open questions in the theory of Lie algebras. We present evidence that there are probably new examples of irreducible target space duality.

hep-th↗
arXiv2000

Target Space Duality I: General Theory

We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and Mtilde arises because of the existence of a very special symplectic manifold. This manifold locally looks like M x Mtilde and admits a double fibration. We analyze the local geometric requirements necessary for target space duality and prove that both manifolds must admit flat orthogonal connections. We show how abelian duality, nonabelian duality and Poisson-Lie duality are all special cases of a more general framework. As an example we exhibit new (nonlinear) dualities in the case M = Mtilde = R^n.

hep-th↗
arXiv1999

Integrable theories in any dimension: a perspective

We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of dimension $d+1$ by the introduction of a $d$-form connection. The method has been used to study several theories of physical interest, like self-dual Yang-Mills theories, Bogomolny equations, non-linear sigma models and Skyrme-type models. The local version of the generalized zero curvature involves a Lie algebra and a representation of it, leading to a number of conservation laws equal to the dimension of that representation. We discuss the conditions a given theory has to satisfy in order for its associated zero curvature to admit an infinite dimensional (reducible) representation. We also present the theory in the more abstract setting of the space of loops, which gives a deeper understanding and a more simple formulation of integrability in any dimension.

hep-th↗