1,209 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
A Note on the Holographic Beta and C Functions
The holographic RG flow in AdS/CFT correspondence naturally defines a
holographic scheme in which the central charge c and the beta function are
related by a universal formula. We perform some checks of that formula and we
compare it with quantum field theory expectations. We discuss alternative
definitions of the c-function. In particular, we compare, for a particular
supersymmetric flow, the holographic c-function with the central charge
computed directly from the two-point function of the stress-energy tensor.Comment: Version accepted for publication in Phys. Lett. B, expanded
introduction. 11 pages, 2 embedded eps figure
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
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
3-D Interacting CFTs and Generalized Higgs Phenomenon in Higher Spin Theories on AdS
We study a duality, recently conjectured by Klebanov and Polyakov, between
higher-spin theories on AdS_4 and O(N) vector models in 3-d. These theories are
free in the UV and interacting in the IR. At the UV fixed point, the O(N) model
has an infinite number of higher-spin conserved currents. In the IR, these
currents are no longer conserved for spin s>2. In this paper, we show that the
dual interpretation of this fact is that all fields of spin s>2 in AdS_4 become
massive by a Higgs mechanism, that leaves the spin-2 field massless. We
identify the Higgs field and show how it relates to the RG flow connecting the
two CFTs, which is induced by a double trace deformation.Comment: 8 pages, latex; v2 references adde
On field theory quantization around instantons
With the perspective of looking for experimentally detectable physical
applications of the so-called topological embedding, a procedure recently
proposed by the author for quantizing a field theory around a non-discrete
space of classical minima (instantons, for example), the physical implications
are discussed in a ``theoretical'' framework, the ideas are collected in a
simple logical scheme and the topological version of the Ginzburg-Landau theory
of superconductivity is solved in the intermediate situation between type I and
type II superconductors.Comment: 27 pages, 5 figures, LaTe
Looking Inside the Mind of Millennial Students: What Do They Know or Not Know about Learning
Metacognition, or insight into one’s own learning process, may be critical for academic success. In this presentation, we cover some of the key metacognitive processes, discussing the areas in which college students often struggle. We address the questions of whether these metacognitive deficiencies are related to brain maturation, developmental stages or educational shortcomings and whether there are any metacognitive issues that are unique to millennial students (i.e., generational effects). Finally, we consider whether millennial characteristics should influence the ways in which we attempt to teach metacognitive skills to the current cohort of students
Renormalization Group Flows from Five-Dimensional Supergravity
The use of gauged supergravity as a tool in studying the
AdS/CFT correspondence for Yang-Mills theory is reviewed. The
supergravity potential implies a non-trivial, supersymmetric IR fixed point,
and the flow to this fixed point is described in terms of a supergravity kink.
The results agree perfectly with earlier, independent field theory results. A
supergravity inspired -function, and corresponding -theorem is discussed
for general flows, and the simplified form for supersymmetric flows is also
given. Flows along the Coulomb branch of the Yang-Mills theory are also
described from the five-dimensional perspective.Comment: 12 pages, 3 figures; Latex, ioplppt.sty, iopl12.sty, epsf.sty.
Contribution to Strings `9
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