Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect

Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two-- and higher--dimensional surfaces (being able to mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero depths). What we have considered is the {\it additional} contribution to the cc coming from the non-trivial topology of space or from specific boundary conditions imposed on braneworld models (kind of cosmological Casimir effects). Assuming someone will be able to prove (some day) that the ground value of the cc is zero, as many had suspected until very recently, we will then be left with this incremental value coming from the topology or BCs. We show that this value can have the correct order of magnitude in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.Comment: 9 pages, 1 figure, Talk given at the Seventh International Workshop Quantum Field Theory under the Influence of External Conditions, QFEXT'05, Barcelona, September 5-9, 200

Zeta-Function Regularization is Uniquely Defined and Well

Hawking's zeta function regularization procedure is shown to be rigorously and uniquely defined, thus putting and end to the spreading lore about different difficulties associated with it. Basic misconceptions, misunderstandings and errors which keep appearing in important scientific journals when dealing with this beautiful regularization method ---and other analytical procedures--- are clarified and corrected.Comment: 7 pages, LaTeX fil

2D Dilaton-Maxwell Gravity as a Fixed Point of the Renormalization Group

A general model of dialton-Maxwell gravity in two dimensions is investigated. The corresponding one-loop effective action and the generalized $\beta$-functions are obtained. A set of models that are fixed points of the renormalization group equations are presented.Comment: 7 pages, LaTeX file, UB-ECM-PF 92/Mar1

General dilatonic gravity with an asymptotically free gravitational coupling constant near two dimensions

We study a renormalizable, general theory of dilatonic gravity (with a kinetic-like term for the dilaton) interacting with scalar matter near two dimensions. The one-loop effective action and the beta functions for this general theory are written down. It is proven that the theory possesses a non-trivial ultraviolet fixed point which yields an asymptotically free gravitational coupling constant (at $\epsilon \rightarrow 0$) in this regime. Moreover, at the fixed point the theory can be cast under the form of a string-inspired model with free scalar matter. The renormalization of the Jackiw-Teitelboim model and of lineal gravity in $2+\epsilon$ dimensions is also discussed. We show that these two theories are distinguished at the quantum level. Finally, fermion-dilatonic gravity near two dimensions is considered.Comment: LaTeX, 13 pages, no figure

Conformal Factor Dynamics in the 1/N Expansion

We suggest to consider conformal factor dynamics as applying to composite boundstates, in frames of the $1/N$ expansion. In this way, a new model of effective theory for quantum gravity is obtained. The renormalization group (RG) analysis of this model provides a framework to solve the cosmological constant problem, since the value of this constant turns out to be suppressed, as a result of the RG contributions. The effective potential for the conformal factor is found too.Comment: 9 pages, LaTeX file, 6-8-1

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.Comment: 11 PAGE

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.Comment: 9 pages, LaTeX file, 3 figures (not included), HUPD-92-10, UB-ECM-PF 92/2

A renormalization group improved non-local gravitational effective Lagrangian

Renormalization group techniques are used in order to obtain the improved non-local gravitational effective action corresponding to any asymptotically free GUT, up to invariants which are quadratic on the curvature. The corresponding non-local gravitational equations are written down, both for the case of asymptotically free GUTs and also for quantum R$^2$-gravity. The implications of the results when obtaining the flux of vacuum radiation through the future null infinity are briefly discussed.Comment: LaTeX file, 11 pages, no figure