Search

We compute the one-loop divergences in a theory of gravity with Lagrangian of the general form $f(R,R_{����}R^{����})$, on an Einstein background. We also establish that the one-loop effective action is invariant under a duality that consists of changing certain parameters in the relation between the metric and the quantum fluctuation field. Finally, we discuss the unimodular version of such a theory and establish its equivalence at one-loop order with the general case., 14 pages, v2:minor corrections, refs. added/modified

We compute the one-loop effective action in unimodular gravity, starting from two different classical formulations of the theory. We find that the effective action is the same in both cases, and agrees with the one of General Relativity.

There have been some speculations about the existence of critical unitary O(N)-invariant scalar field theories in dimensions 4, 5 pages, 4 figures, expanded introduction, in press on PRD

Any theory can be made Weyl invariant by introducing a dilaton. It is shown how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely for the one loop beta functions of a dilaton conformally coupled to a dynamical metric, but the results have wider validity. This formalism could be used to define the meaning of a theory with a position-dependent cutoff: it is equivalent to a theory with a constant cutoff, but a conformally related metric., Comment: To appear in New Journal of Physics. 20 pages

We consider the standard model without the Higgs boson, where the Goldstone modes are described by a nonlinear sigma model. We study the renormalization group flow of the sigma model coupling f and of the electroweak parameters S and T. The condition that the couplings reach a fixed point at high energy leaves the low energy values of f and T arbitrary (to be determined experimentally) and fixes S to a value compatible with electroweak precision data., Comment: 4 pages, 2 figures

We study the beta functions of the leading, two-derivative terms of the left-gauged SU(N) nonlinear sigma-model in d dimensions. In d>2, we find the usual Gaussian ultraviolet fixed point for the gauge coupling and an attractive non-Gaussian fixed point for the Goldstone boson coupling. The position of the latter fixed point controls the chiral expansion, unitarity and the strength of the tree-level Goldstone boson scattering amplitudes. Attention is paid to the gauge- and scheme-dependence of the results., REVTeX4, 11 pages, no figures, v2. Revised version accepted for publication in PRD where comments on large N have been removed

Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For $d>2$ and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned., 9 pages

Asymptotic safety is a set of conditions, based on the existence of a nontrivial fixed point for the renormalization group flow, which would make a quantum field theory consistent up to arbitrarily high energies. After introducing the basic ideas of this approach, I review the present evidence in favor of an asymptotically safe quantum field theory of gravity., Comment: In "Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter", ed. D. Oriti, Cambridge University Press A sign corrected in eq. (1.4.7), a reference updated

Nonlinear sigma models arise in supergravity theories with or without matter couplings in various dimensions and they are important in understanding the duality symmetries of M-theory. With this motivation in mind, we review the salient features of gauged and ungauged nonlinear sigma models with or without Wess-Zumino terms for general target spaces in a minimal as well as lifted formulation. Relevant to the question of finding interesting vacua of gauged supergravity theories is the highly constrained potential which arises naturally in these theories. Motivated by this fact, we derive a general and simple formula for a gauge invariant potential of this kind., Comment: 24 pages, latex, uses sprocl.sty, contribution to the R. Arnowitt Fest: A Symposium on Supersymmetry and Gravitation, College Station, TX, 5-7 April 1998

We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects., 13 pages, plainTex

There is a general mechanism by which certain matter fields coupled to gravity can generate a nontrivial effective potential for the conformal factor of the metric. It is based on a nonstandard regularization method, with the cutoff being defined independently of the conformal factor. This mechanism produces a coupling of the matter fields to a dilaton, and a complicated interaction between matter, dilaton and metric. When it is applied to the standard model, it gives an effective potential which can be used to predict the top and Higgs masses. If the purely gravitational contribution to the potential is added, the mass of the dilaton is of the order of Planck's mass and the large hierarchy between the Planck and Fermi scales appears to be due to the smallness of the Higgs-dilaton coupling., Comment: 7 pages, plain TEX, ITP and SISSA

The algebra W_{1+\infty} with central charge c=0 can be identified with the algebra of quantum observables of a particle moving on a circle. Mathematically, it is the universal enveloping algebra of the Euclidean algebra in two dimensions. Similarly, the super W_\infty algebra is found to be the universal enveloping algebra of the super-Euclidean algebra in two dimensions., Comment: (8 pages)

We show how to obtain a single chiral family of an SO(10) GUT, starting from a Majorana-Weyl representation of a unifying ("GraviGUT") group SO(3,11), which contains the gravitational Lorentz group SO(3,1). An action is proposed, which reduces to the correct fermionic GUT action in the broken phase., Comment: 7 pages. Discussion clarified. Version matching the published one

The coupling of chiral fermions to gravity makes use only of the selfdual SU(2) subalgebra of the (complexified) SO(3,1) algebra. It is possible to identify the antiselfdual subalgebra with the SU(2)_L isospin group that appears in the Standard Model, or with its right-handed counterpart SU(2)_R that appears in some extensions. Based on this observation, we describe a form of unification of the gravitational and weak interactions. We also discuss models with fermions of both chiralities, the inclusion strong interactions, and the way in which these unified models of gravitational and gauge interactions avoid conflict with the Coleman-Mandula theorem., 18 pages, typos corrected and improved wording