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

Higher-spin current multiplets in operator-product expansions

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.Comment: 19 pages. Introductory paragraph, misprint corrected and updated references. CQG in pres

Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility

I discuss several issues about the irreversibility of the RG flow and the trace anomalies c, a and a'. First I argue that in quantum field theory: i) the scheme-invariant area Delta(a') of the graph of the effective beta function between the fixed points defines the length of the RG flow; ii) the minimum of Delta(a') in the space of flows connecting the same UV and IR fixed points defines the (oriented) distance between the fixed points; iii) in even dimensions, the distance between the fixed points is equal to Delta(a)=a_UV-a_IR. In even dimensions, these statements imply the inequalities 0 =< Delta(a)=< Delta(a') and therefore the irreversibility of the RG flow. Another consequence is the inequality a =< c for free scalars and fermions (but not vectors), which can be checked explicitly. Secondly, I elaborate a more general axiomatic set-up where irreversibility is defined as the statement that there exist no pairs of non-trivial flows connecting interchanged UV and IR fixed points. The axioms, based on the notions of length of the flow, oriented distance between the fixed points and certain "oriented-triangle inequalities", imply the irreversibility of the RG flow without a global a function. I conjecture that the RG flow is irreversible also in odd dimensions (without a global a function). In support of this, I check the axioms of irreversibility in a class of d=3 theories where the RG flow is integrable at each order of the large N expansion.Comment: 24 pages, 3 figures; expanded intro, improved presentation, references added - CQ

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

Renormalizable acausal theories of classical gravity coupled with interacting quantum fields

We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced number of independent couplings. An interesting class of models is obtained from ordinary power-counting renormalizable theories, letting the couplings depend on the scalar curvature R of spacetime. The divergences are removed without introducing higher-derivative kinetic terms in the gravitational sector. The metric tensor has a non-trivial running, even if it is not quantized. The results are proved applying a certain map that converts classical instabilities, due to higher derivatives, into classical violations of causality, whose effects become observable at sufficiently high energies. We study acausal Einstein-Yang-Mills theory with an R-dependent gauge coupling in detail. We derive all-order formulas for the beta functions of the dimensionality-six gravitational vertices induced by renormalization. Such beta functions are related to the trace-anomaly coefficients of the matter subsector.Comment: 36 pages; v2: CQG proof-corrected versio

Search for flow invariants in even and odd dimensions

A flow invariant in quantum field theory is a quantity that does not depend on the flow connecting the UV and IR conformal fixed points. We study the flow invariance of the most general sum rule with correlators of the trace Theta of the stress tensor. In even (four and six) dimensions we recover the results known from the gravitational embedding. We derive the sum rules for the trace anomalies a and a' in six dimensions. In three dimensions, where the gravitational embedding is more difficult to use, we find a non-trivial vanishing relation for the flow integrals of the three- and four-point functions of Theta. Within a class of sum rules containing finitely many terms, we do not find a non-vanishing flow invariant of type a in odd dimensions. We comment on the implications of our results.Comment: 21 pages, v2: expanded introduction, published in NJ

Four-dimensional topological Einstein-Maxwell gravity

The complete on-shell action of topological Einstein-Maxwell gravity in four-dimensions is presented. It is shown explicitly how this theory for SU(2) holonomy manifolds arises from four-dimensional Euclidean N=2 supergravity. The twisted local BRST symmetries and twisted local Lorentz symmetries are given and the action and stress tensor are shown to be BRST-exact. A set of BRST-invariant topological operators is given. The vector and antisymmetric tensor twisted supersymmetries and their algebra are also found.Comment: Published version. Expanded discussion of new results in the introduction and some clarifying remarks added in later sections. 22 pages, uses phyzz

The Non-Perturbative N=2{\cal N} = 2 SUSY Yang-Mills Theory from Semiclassical Absorption of Supergravity by Wrapped D Branes

The imaginary part of the two point functions of the superconformal anomalous currents are extracted from the cross-sections of semiclassical absorption of dilaton, RR-2 form and gravitino by the wrapped D5 branes. From the central terms of the two point functions anomalous Ward identity is established which relates the exact pre-potential of the ${\cal N}=2$ SUSY Yang-Mills theory with the vacuum expectation value of the anomaly multiplet. From the Ward identity, WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equation can be derived which is solved for the exact pre-potential.Comment: 11 pages, late

Operator mixing in N=4 SYM: The Konishi anomaly revisited

In the context of the superconformal N=4 SYM theory the Konishi anomaly can be viewed as the descendant $K_{10}$ of the Konishi multiplet in the 10 of SU(4), carrying the anomalous dimension of the multiplet. Another descendant $O_{10}$ with the same quantum numbers, but this time without anomalous dimension, is obtained from the protected half-BPS operator $O_{20'}$ (the stress-tensor multiplet). Both $K_{10}$ and $O_{10}$ are renormalized mixtures of the same two bare operators, one trilinear (coming from the superpotential), the other bilinear (the so-called "quantum Konishi anomaly"). Only the operator $K_{10}$ is allowed to appear in the right-hand side of the Konishi anomaly equation, the protected one $O_{10}$ does not match the conformal properties of the left-hand side. Thus, in a superconformal renormalization scheme the separation into "classical" and "quantum" anomaly terms is not possible, and the question whether the Konishi anomaly is one-loop exact is out of context. The same treatment applies to the operators of the BMN family, for which no analogy with the traditional axial anomaly exists. We illustrate our abstract analysis of this mixing problem by an explicit calculation of the mixing matrix at level g^4 ("two loops") in the supersymmetric dimensional reduction scheme.Comment: 28 pp LaTeX, 3 figure