Deformed dimensional regularization for odd (and even) dimensional theories

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of an odd product of gamma matrices in odd dimensions. The regularization is completed with an evanescent higher-derivative deformation, which proves to be efficient in practical computations. This technique is particularly convenient in three dimensions for Chern-Simons gauge fields, two-component fermions and four-fermion models in the large N limit, eventually coupled with quantum gravity. Differently from even dimensions, in odd dimensions it is not always possible to have propagators with fully Lorentz invariant denominators. The main features of the deformed technique are illustrated in a set of sample calculations. The regularization is universal, local, manifestly gauge-invariant and Lorentz invariant in the physical sector of spacetime. In flat space power-like divergences are set to zero by default. Infinitely many evanescent operators are automatically dropped.Comment: 27 pages, 3 figures; v2: expanded presentation of some arguments, IJMP

Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding

Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is particularly meaningful in the class of Weyl instantons, is introduced. The topological embedding, a theoretical framework for constructing physical amplitudes that are well-defined order by order in perturbation theory around instantons, is explicitly applied to the computation of the correlation functions of Dirac fermions in a punctured gravitational background, as well as to the most general QED and QCD amplitude. Various alternatives are worked out, discussed and compared. The quantum background affects the propagation by generating a certain effective ``quantum'' metric. The topological embedding could represent a new chapter of quantum field theory.Comment: LaTeX, 18 pages, no figur

A universal flow invariant in quantum field theory

A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories, scale invariance is broken by quantum effects and the flow invariant a_{UV}-a_{IR} is measured by the area of the graph of the beta function between the fixed points. There exists a theoretical explanation of this fact. On the other hand, when scale invariance is broken at the classical level, it is empirically known that the flow invariant equals c_{UV}-c_{IR} in massive free-field theories, but a theoretical argument explaining why it is so is still missing. A number of related open questions are answered here. A general formula of the flow invariant is found, which holds also when the stress tensor has improvement terms. The conditions under which the flow invariant equals c_{UV}-c_{IR} are identified. Several non-unitary theories are used as a laboratory, but the conclusions are general and an application to the Standard Model is addressed. The analysis of the results suggests some new minimum principles, which might point towards a better understanding of quantum field theory.Comment: 28 pages, 3 figures; proof-corrected version for CQ

Consistent irrelevant deformations of interacting conformal field theories

I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an infinite number of lagrangian terms and a finite number of independent parameters that renormalize coherently. The coefficients of the irrelevant terms are determined imposing that the beta functions of the dimensionless combinations of couplings vanish ("quasi-finiteness equations"). The expansion in powers of the energy is meaningful for energies much smaller than an effective Planck mass. Multiple deformations can be considered also. I study the general conditions to have non-trivial solutions. As an example, I construct the Pauli deformation of the IR fixed point of massless non-Abelian Yang-Mills theory with N_c colors and N_f <~ 11N_c/2 flavors and compute the couplings of the term F^3 and the four-fermion vertices. Another interesting application is the construction of finite chiral irrelevant deformations of N=2 and N=4 superconformal field theories. The results of this paper suggest that power-counting non-renormalizable theories might play a role in the description of fundamental physics.Comment: 23 pages, 5 figures; reference updated - JHE

Tailoring Dielectric Properties of Multilayer Composites Using Spark Plasma Sintering

A straightforward and simple way to produce well-densified ferroelectric ceramic composites with a full control of both architecture and properties using spark plasma sintering (SPS) is proposed. SPS main outcome is indeed to obtain high densification at relatively low temperatures and short treatment times thus limiting interdiffusion in multimaterials. Ferroelectric/dielectric (BST64/MgO/BST64) multilayer ceramic densified at 97% was obtained, with unmodified Curie temperature, a stack dielectric constant reaching 600, and dielectric losses dropping down to 0.5%, at room-temperature. This result ascertains SPS as a relevant tool for the design of functional materials with tailored properties

Covariant Pauli-Villars Regularization of Quantum Gravity at the One Loop Order

We study a regularization of the Pauli-Villars kind of the one loop gravitational divergences in any dimension. The Pauli-Villars fields are massive particles coupled to gravity in a covariant and nonminimal way, namely one real tensor and one complex vector. The gauge is fixed by means of the unusual gauge-fixing that gives the same effective action as in the context of the background field method. Indeed, with the background field method it is simple to see that the regularization effectively works. On the other hand, we show that in the usual formalism (non background) the regularization cannot work with each gauge-fixing.In particular, it does not work with the usual one. Moreover, we show that, under a suitable choice of the Pauli-Villars coefficients, the terms divergent in the Pauli-Villars masses can be corrected by the Pauli-Villars fields themselves. In dimension four, there is no need to add counterterms quadratic in the curvature tensor to the Einstein action (which would be equivalent to the introduction of new coupling constants). The technique also works when matter is coupled to gravity. We discuss the possible consequences of this approach, in particular the renormalization of Newton's coupling constant and the appearance of two parameters in the effective action, that seem to have physical implications.Comment: 26 pages, LaTeX, SISSA/ISAS 73/93/E

More on the Subtraction Algorithm

We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions $\delta\lambda$ of the parameters $\lambda$ of the classical Lagrangian and canonical transformations, by generalizing a well- known conjecture on the form of the divergent terms. We also show that it is possible to reach a complete control on the effects of the subtraction algorithm on the space ${\cal M}_{gf}$ of the gauge-fixing parameters. A principal fiber bundle ${\cal E}\rightarrow {\cal M}_{gf}$ with a connection $\omega_1$ is defined, such that the canonical transformations are gauge transformations for $\omega_1$. This provides an intuitive geometrical description of the fact the on shell physical amplitudes cannot depend on ${\cal M}_{gf}$. A geometrical description of the effect of the subtraction algorithm on the space ${\cal M}_{ph}$ of the physical parameters $\lambda$ is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on ${\cal M}_{ph}$, orthogonal to ${\cal M}_{gf}$ (under which the action transforms as a scalar), and gauge transformations on ${\cal E}$. In this geometrical context, a suitable concept of predictivity is formulated. We give some examples of (unphysical) toy models that satisfy this requirement, though being neither power counting renormalizable, nor finite.Comment: LaTeX file, 37 pages, preprint SISSA/ISAS 90/94/E

Master Functional And Proper Formalism For Quantum Gauge Field Theory

We develop a general field-covariant approach to quantum gauge theories. Extending the usual set of integrated fields and external sources to "proper" fields and sources, which include partners of the composite fields, we define the master functional Omega, which collects one-particle irreducible diagrams and upgrades the usual Gamma-functional in several respects. The functional Omega is determined from its classical limit applying the usual diagrammatic rules to the proper fields. Moreover, it behaves as a scalar under the most general perturbative field redefinitions, which can be expressed as linear transformations of the proper fields. We extend the Batalin-Vilkovisky formalism and the master equation. The master functional satisfies the extended master equation and behaves as a scalar under canonical transformations. The most general perturbative field redefinitions and changes of gauge-fixing can be encoded in proper canonical transformations, which are linear and do not mix integrated fields and external sources. Therefore, they can be applied as true changes of variables in the functional integral, instead of mere replacements of integrands. This property overcomes a major difficulty of the functional Gamma. Finally, the new approach allows us to prove the renormalizability of gauge theories in a general field-covariant setting. We generalize known cohomological theorems to the master functional and show that when there are no gauge anomalies all divergences can be subtracted by means of parameter redefinitions and proper canonical transformations.Comment: 32 pages; v2: minor changes and proof corrections, EPJ

A review of the role of ultrasound biomicroscopy in glaucoma associated with rare diseases of the anterior segment

Ultrasound biomicroscopy is a non-invasive imaging technique, which allows high-resolution evaluation of the anatomical features of the anterior segment of the eye regardless of optical media transparency. This technique provides diagnostically significant information in vivo for the cornea, anterior chamber, chamber angle, iris, posterior chamber, zonules, ciliary body, and lens, and is of great value in assessment of the mechanisms of glaucoma onset. The purpose of this paper is to review the use of ultrasound biomicroscopy in the diagnosis and management of rare diseases of the anterior segment such as mesodermal dysgenesis of the neural crest, iridocorneal endothelial syndrome, phakomatoses, and metabolic disorders

Heavy-traffic revenue maximization in parallel multiclass queues

Motivated by revenue maximization in server farms with admission control, we investigate the optimal scheduling in parallel processor-sharing queues. Incoming customers are distinguished in multiple classes and we define revenue as a weighted sum of class throughputs. Under these assumptions, we describe a heavy-traffic limit for the revenue maximization problem and study the asymptotic properties of the optimization model as the number of clients increases. Our main result is a simple heuristic that is able to provide tight guarantees on the optimality gap of its solutions. In the general case with M queues and R classes, we prove that our heuristic is (1+1M-1)-competitive in heavy-traffic. Experimental results indicate that the proposed heuristic is remarkably accurate, despite its negligible computational costs, both in random instances and using service rates of a web application measured on multiple cloud deployments