850 research outputs found
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 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 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 of the Konishi multiplet in the 10 of
SU(4), carrying the anomalous dimension of the multiplet. Another descendant
with the same quantum numbers, but this time without anomalous
dimension, is obtained from the protected half-BPS operator (the
stress-tensor multiplet). Both and 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
is allowed to appear in the right-hand side of the Konishi anomaly
equation, the protected one 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
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