15952552
Renormalization of crumpled manifolds.
We consider a model of a D-dimensional tethered manifold interacting by excluded volume in ${\mathit{openR}}^{\mathit{d}}$ with a single point. By use of intrinsic distance geometry, we first provide a rigorous definition of the analytic continuation of its perturbative expansion for arbitrary D, 0D2. We then construct explicitly a renormalization operation ssR, ensuring renormalizability to all orders. This is the first example of mathematical construction and renormalization for an interacting extended object with continuous internal dimension, encompassing field theory.
119623671
Instanton Calculus for the Self-Avoiding Manifold Model
We compute the normalisation factor for the large order asymptotics of perturbation theory for the self-avoiding manifold (SAM) model describing flexible tethered (D-dimensional) membranes in d-dimensional space, and the ε-expansion for this problem. For that purpose, we develop the methods inspired from instanton calculus, that we introduced in a previous publication (Nucl. Phys. B 534 (1998) 555), and we compute the functional determinant of the fluctuations around the instanton configuration. This determinant has UV divergences and we show that the renormalized action used to make perturbation theory finite also renders the contribution of the instanton UV-finite. To compute this determinant, we develop a systematic large-d expansion. For the renormalized theory, we point out problems in the interplay between the limits ε→ 0 and d→∞, as well as IR divergences when ε=0. We show that many cancellations between IR divergences occur, and argue that the remaining IR-singular term is associated to amenable non-analytic contributions in the large-d limit when ε=0. The consistency with the standard instanton-calculus results for the self-avoiding walk is checked for D=1.
121828238
A comment on induced gravity
Abstract Because of the non-perturbative ambiguity of the stress-energy tensor in theories with dynamical breaking of conformal invariance, there is no unique self-consistent way to compute the Newton's and cosmological constants of the corresponding induced gravitation theories, when leading quadratic or quartic divergences are present.
121525452
On the ambiguity of composite operators, IR renormalons and the status of the operator product expansion
Abstract It is not possible in general to define in an unambiguous way the vacuum expectation value of local operators such that 〈0|Tr G μν G μν |0〉 used in the QCD sum rules formalism. This phenomenon is exhibited via the 1/ N expansion of some two-dimensional models and explains the existence of IR singularities (renormalons) in the Borel plane. Such ambiguities are present in the general definition of composite operators in any UV free theory. The consequences for the status of the operator product expansion are discussed.
123656602
Critical exponents in a model of dynamically triangulated random surfaces
Abstract We calculate the mass gap and the susceptibility critical exponents, in a model of dynamically triangulated random surfaces, for various values of the model parameters. Strong coupling series as well as Monte Carlo simulation are used and we carefully compare results obtained with the two methods. The transitions between different phases of the model are examined.
38308310
Comment on "Superinstantons and the reliability of perturbation theory in non-Abelian models"
In a recent letter (hep-lat/9311019) A. Patrascioiu and E. Seiler argued that when taking into account "superinstantons configurations" the perturbative expansion and the beta-function of the two-dimensional non-linear sigma-model are modified at two loops order. I point out that: (1) perturbation theory in a superinstanton background is infra-red singular beyond three loops; (2) the new infra-red singular terms, which change the two loop terms, come from singular operators - describing superinstanton insertions - in the OPE; (3) taking into account these operators, the beta-function is not modified. Therefore the results of Patrascioiu and Seiler do not contradict perturbation theory.
44187843
Linear Instability of Non-vacuum Spacetimes *
We study the problem of linear instability in non-vacuum spacetimes. For vacuum spa.cetimes linear instability occurs when the spacetime has Killing vectors. In the non-vacuum case, one must prescribe how the sources are to vary. For one natural choice, we show that the signal for instability is the existence of Integral Constraint Vector fields. These vector fields lead, as in the vacuum case, to nonlinear constraints on the first order perturbations to the metric and momentum. For other choices for variations of the sources, we show how to modify the definition of Integral Constra,int Vectors appropriately. Since Robertson-Walker spacetimes have Integral Constraint Vectors our results may have cosmological applications.