Searcharxiv⌕ Search

arXiv subjects

E. Elizalde

Publications and source records attributed to E. Elizalde.

161 records · Page 9Linked to original sources
arXiv1993

Partition Functions for the Rigid String and Membrane at Any Temperature

Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and written as asymptotic sums of Riemann-Hurwitz zeta functions, which provide very good numerical approximations with just a few first terms. This allows to obtain systematic corrections to the results of Polchinski et al., corresponding to the limits $T\rightarrow 0$ and $T\rightarrow \infty$ of the rigid string, and to analyze the intermediate range of temperatures. In particular, a way to obtain the Hagedorn temperature for the rigid membrane is thus found.

hep-th↗
arXiv1993

Mellin Transform Techniques for Zeta-Function Resummations

Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the result is naturally split into the same three contributions of very different nature, i.e. the series of Riemann zeta functions and the power and negative exponentially behaved functions, respectively, well known from the original proof. The new theorem deals equally well with elliptic differential operators whose spectrum is not explicitly known. Rigorous results on the asymptoticity of the outcoming series are given, together with some specific examples. Exact analytical formulas, simplifying approximations and numerical estimates for the last of the three contributions (the most difficult to handle) are obtained. As an application of the method, the summation of the series which appear in the analytic computation (for different ranges of temperature) of the partition function of the string ---basic in order to ascertain if QCD is some limit of a string theory--- is PERFORMED.

hep-th↗
arXiv1993

Renormalization-group improved effective potential for gauge theories in curved spacetime

The renormalization-group improved effective potential for an arbitrary renormalizable massless gauge theory in curved spacetime is found,thus generalizing Coleman-Weinberg's approach corresponding to flat space.Some explicit examples are considered,among of them:scalar self-interacting theory,scalar electrody namics,the asymptotically-free SU(2) gauge model,and the SU(5) GUT theory. The possibility of curvature-induced phase transitions is analyzed.It is shown that such a phase transition may take place in a SU(5) inflationary universe.The inclusion of quantum gravity effects isbriefly discussed.

hep-th↗
arXiv1993

Convenient Versus Unique Effective Action Formalism in 2D Dilaton-Maxwell Quantum Gravity

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effective action are calculated in three different covariant gauges: (i) De Witt, (ii) $Ω$-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of the $S$-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.

hep-th↗
arXiv1992

One Loop Counterterms in 2D Dilaton-Maxwell Quantum Gravity

The renormalization structure of two-dimensional quantum gravity is investigated, in a covariant gauge. One-loop divergences of the effective action are calculated. All the surface divergent terms are taken into account, thus completing previous one-loop calculations of the theory. It is shown that the on-shell effective action contains only surface divergences. The off-shell renormalizability of the theory is discussed and classes of renormalizable dilaton and Maxwell potentials are found.

hep-th↗
arXiv1992

Spectral Zeta Functions for Spherical Aharonov-Bohm Quantum Bags

We study the sum $\dsζ_H(s)=\sum_j E_j^{-s}$ over the eigenvalues $E_j$ of the Schrdinger equation in a spherical domain with Dirichlet walls, threaded by a line of magnetic flux. Rather than using Green's function techniques, we tackle the mathematically nontrivial problem of finding exact sum rules for the zeros of Bessel functions $J_ν$, which are extremely helpful when seeking numerical approximations to ground state energies. These results are particularly valuable if $ν$ is neither an integer nor half an odd one.

hep-th↗
arXiv1992

A Finite-Temperature Periodic Structure in (SUPER)STRING Theory

Using a Laurent series representation for the (super)string one-loop free energy, an explicit form for the analytic continuation of the Laurent series beyond the critical (Hagedorn) temperature is obtained. As an additional result, a periodic structure is found in (super)string thermodynamics. A brief physical discussion about the origin and meaning of such structure is carried out.

hep-th↗
arXiv1992

Gravitational Phase Transitions in Infrared Quantum Gravity

The conformal anomaly induced sector of four-dimensional quantum gravity (infrared quantum gravity) ---which has been introduced by Antoniadis and Mottola--- is here studied on a curved fiducial background. The one-loop effective potential for the effective conformal factor theory is calculated with accuracy, including terms linear in the curvature. It is proven that a curvature induced phase transition can actually take place. An estimation of the critical curvature for different choices of the parameters of the theory is given.

hep-th↗
arXiv1992

A Novel Representation for the Free Energy in String Theory at Non-Zero Temperature

A novel representation ---in terms of a Laurent series--- for the free energy of string theory at non-zero temperature is constructed. The examples of open bosonic, open supersymmetric and closed bosonic strings are studied in detail. In all these cases the Laurent series representation for the free energy is obtained explicitly. It is shown that the Hagedorn temperature arises in this formalism as the convergence condition (specifically, the radius of convergence) of the corresponding Laurent series. Some prospects for further applications are also discussed. In particular, an attempt to describe string theory above the Hagedorn temperature ---via Borel analytical continuation of the Laurent series representation--- is provided.

hep-th↗
arXiv1992

Laurent Series Representation for the Open Superstring Free Energy

Open superstrings at non-zero temperature are considered. A novel representation for the free energy (Laurent series representation) is constructed. It is shown that the Hagedorn temperature arises in this formalism as the convergence condition (specifically, the radius of convergence) of the Laurent series.

hep-th↗
arXiv1992

One-Loop Renormalization in Two-Dimensional Matter-Dilaton Quantum Gravity and Charged Black Holes

The quantum properties of two-dimensional matter-dilaton gravity ---which includes a large family of actions for two-dimensional gravity (in particular, string-inspired models)--- are investigated. The one-loop divergences in linear covariant gauges are calculated and the structure of the one-loop renormalization is studied. The explicit forms of the dilaton potential, dilaton-Maxwell, and dilaton-scalar couplings for which the theory is one-loop multiplicatively renormalizable are found. A comparison with the one-loop renormalization structure of four-dimensional gravity-matter theory is given. Charged multiple-horizon black holes which appear in the model are also considered.

hep-th↗
arXiv1992

One-loop divergences in two-dimensional Maxwell-dilaton quantum gravity

Two-dimensional Maxwell-dilaton quantum gravity, which covers a large family of the actions for two-dimensional gravity (in particular, string-inspired models) is investigated. Charged black holes which appear in the theory are briefly discussed. The one-loop divergences in the linear covariant gauges are calculated. It is shown that for some choices of the dilaton potential and dilaton-Maxwell coupling, the theory is one-loop multiplicatively renormalizable (or even finite). A comparison with the divergences structure of four-dimensional Einstein-Maxwell gravity is given.

hep-th↗
arXiv1992

Effective potential and stability of the rigid membrane

The calculation of the effective potential for fixed-end and toroidal rigid $p$-branes is performed in the one-loop as well as in the $1/d$ approximations. The analysis of the involved zeta-functions (of inhomogeneous Epstein type) which appear in the process of regularization is done in full detail. Assymptotic formulas (allowing only for exponentially decreasing errors of order $\leq 10^{-3}$) are found which carry all the dependences on the basic parameters of the theory explicitly. The behaviour of the effective potential (specified to the membrane case $p=2$) is investigated, and the extrema of this effective potential are obtained.

hep-th↗
arXiv1992

Spontaneous compactification in 2D induced quantum gravity

Spontaneous compactification ---on a $R^1\times S^1$ background--- in 2D induced quantum gravity (considered as a toy model for more fundamental quantum gravity) is analyzed in the gauge-independent effective action formalism. It is shown that such compactification is stable, in contradistinction to multidimensional quantum gravity on a $R^D\times S^1 \ (D>2)$ background ---which is known to be one-loop unstable.

hep-th↗
arXiv1992

Renormalization group equations in curved space-time with non-trivial Topology

Renormalization group equations for massless GUT's in curved space-time with non-trivial topology are formulated. The asymptotics of the effective action both at high and low energies are obtained. It is shown that the Casimir energy contribution at high curvature (early Universe) becomes non-essential in the effective action.

hep-th↗