arXiv subjects

Alvaro Restuccia

Publications and source records attributed to Alvaro Restuccia.

28 records · Page 2Linked to original sources

arXiv2012

Non-perturbative analysis of the gravitational energy in Hořava Theory

We perform a non-perturbative analysis of the constraints of the Hořava Gravitational theory. In distinction to Einstein gravity the theory has constraints of the first class together with second class ones. We analyze the consequences of having to impose second classes constraints at any time in the quantum formulation of the theory. The second class constraints are formulated as strongly elliptic partial differential equations allowing a global analysis on the existence and uniqueness of the solution. We discuss the possibility of formulating the theory in terms of a master action with first class constraints only. In this case the Hořava theory would correspond to a gauged fixed version of the master theory. Finally we obtain, using the non-perturbative solution of the constraints, the explicit expression of the gravitational energy. It is, under some assumptions, always positive and the solution of Hořava field equations at minimal energy is the Minkowski metric.

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arXiv2012

Non-perturbative analysis of the constraints and the positivity of the energy of the complete Horava theory

We perform a non-perturbative analysis to the Hamiltonian constraint of the lowest-order effective action of the complete Horava theory, which includes a (\partial_i \ln N)^2 term in the Lagrangian. We cast this constraint as a partial differential equation for N and show that the solution exists and is unique under a condition of positivity for the metric and its conjugate momentum. We interpret this condition as the analog of the positivity of the spatial scalar curvature in general relativity. From the analysis we extract several general properties of the solution for N: an upper bound on its absolute value and its asymptotic behavior. In particular, we find that the asymptotic behavior is different to that of general relativity, which has consequences on the evolution of the initial data and the calculus of variations. Similarly, we proof the existence and uniqueness of the solution of the equation for the Lagrange multiplier of the theory. We also find a relationship between the expression of the energy and the solution of the Hamiltonian constraint. Using it we prove the positivity of the energy of the effective action under consideration. Minkowski spacetime is obtained from Horava theory at minimal energy.

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arXiv2012

On the consistency of the Horava Theory

With the goal of giving evidence for the theoretical consistency of the Horava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Horava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant lambda. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of lambda deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model.

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arXiv2011

Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory

We perform the Hamiltonian analysis for the lowest-order effective action, up to second order in derivatives, of the complete Horava theory. The model includes the invariant terms that depend on \partial_i ln N proposed by Blas, Pujolas and Sibiryakov. We show that the algebra of constraints closes. The "Hamiltonian" constraint is of second-class behavior and it can be regarded as an elliptic partial differential equation for N. The linearized version of this equation is a Poisson equation for N that can be solved consistently. The preservation in time of the Hamiltonian constraint yields an equation that can be consistently solved for a Lagrange multiplier of the theory. The model has six propagating degrees of freedom in the phase space, corresponding to three even physical modes. When compared with the λR model studied by us in a previous paper, it lacks two second-class constraints, which leads to the extra even mode.

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arXiv2011

Spectral properties in supersymmetric matrix models

We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-su-persymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.

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arXiv2011

Closure of the algebra of constraints for a nonprojectable Hořava model

We perform the Hamiltonian analysis for a nonprojectable Horava model whose potential is composed of R and R^2 terms. We show that Dirac's algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Hořava theory, the validity of the full nonprojectable theory still remains unanswered.

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arXiv2009

Local well-posedness for membranes in the light cone gauge

In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution equations is found, which is hyperbolic and has a well-posed initial value problem. We are thus able to solve the initial value problem for the Hamiltonian evolution equations by means of this equivalent system. We furthermore obtain a blowup criterion for the membrane evolution equations, and show, making use of the constraint, that one may achieve improved regularity estimates.

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arXiv2005

The heat kernel of the compactified D=11 supermembrane with non-trivial winding

We study the quantization of the regularized hamiltonian, $H$, of the compactified D=11 supermembrane with non-trivial winding. By showing that $H$ is a relatively small perturbation of the bosonic hamiltonian, we construct a Dyson series for the heat kernel of $H$ and prove its convergence in the topology of the von Neumann-Schatten classes so that $e^{-Ht}$ is ensured to be of finite trace. The results provided have a natural interpretation in terms of the quantum mechanical model associated to regularizations of compactified supermembranes. In this direction, we discuss the validity of the Feynman path integral description of the heat kernel for D=11 supermembranes and obtain a matrix Feynman-Kac formula.

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arXiv1994

Topological Selection of World Manifolds for a P-Brane in a BF--Field

We study the interaction between a $p$-brane and $BF$ system constituted by a $(p+1)$-form and a $n-(p+2)$-form B with a metric independent action on a manifold $M^n$. We identify the allowed $(p+1)$-world manifolds sweeped by the $p$-brane as those restricted by the topological condition of being the boundaries of chains in $M^n$. We find the general solutions of the equation of motion for the field configurations. The solutions for the $B$ field are closely related to the external field configurations that describe the defects needed for the computation of soliton correlation functions.The particular cases of the particle and string evolution are discussed with some detail.

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arXiv1994

Canonical Covariant Formulation of Green-Schwarz Superstring without Second Class Constraints

We describe a canonical covariant formulation of the Green-Schwarz Superstring which allows the construction of a new covariant action canonically equivalent to the Green-Schwarz action but subjected only to first class constraints. From this action the correct BRST operator for the quantization of the Green-Schwarz Superstring may be constructed. Also the gauge fixed action in the Light-Cone gauge may be reobtained. The action presented in this letter generalizes in a non-trivial form the action introduced by Kallosh for the Brink-Schwarz-Casalbuoni Superparticle.

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