1,983 research outputs found
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
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
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
Relevance of the weak equivalence principle and experiments to test it: lessons from the past and improvements expected in space
Tests of the Weak Equivalence Principle (WEP) probe the foundations of
physics. Ever since Galileo in the early 1600s, WEP tests have attracted some
of the best experimentalists of any time. Progress has come in bursts, each
stimulated by the introduction of a new technique: the torsion balance, signal
modulation by Earth rotation, the rotating torsion balance. Tests for various
materials in the field of the Earth and the Sun have found no violation to the
level of about 1 part in 1e13. A different technique, Lunar Laser Ranging
(LLR), has reached comparable precision. Today, both laboratory tests and LLR
have reached a point when improving by a factor of 10 is extremely hard. The
promise of another quantum leap in precision rests on experiments performed in
low Earth orbit. The Microscope satellite, launched in April 2016 and currently
taking data, aims to test WEP in the field of Earth to 1e-15, a 100-fold
improvement possible thanks to a driving signal in orbit almost 500 times
stronger than for torsion balances on ground. The `Galileo Galilei' (GG)
experiment, by combining the advantages of space with those of the rotating
torsion balance, aims at a WEP test 100 times more precise than Microscope, to
1e-17. A quantitative comparison of the key issues in the two experiments is
presented, along with recent experimental measurements relevant for GG. Early
results from Microscope, reported at a conference in March 2017, show
measurement performance close to the expectations and confirm the key role of
rotation with the advantage (unique to space) of rotating the whole spacecraft.
Any non-null result from Microscope would be a major discovery and call for
urgent confirmation; with 100 times better precision GG could settle the matter
and provide a deeper probe of the foundations of physics.Comment: To appear: Physics Letters A, special issue in memory of Professor
Vladimir Braginsky, 2017. Available online:
http://dx.doi.org/10.1016/j.physleta.2017.09.02
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
A TOPOLOGICAL LAGRANGIAN FOR MONOPOLES ON FOUR-MANIFOLDS
We present a topological quantum field theory which corresponds to the moduli
problem associated to Witten's monopole equations for four-manifolds. The
construction of the theory is carried out in purely geometrical terms using the
Mathai-Quillen formalism, and the corresponding observables are described.
These provide a rich set of new topological quantites.Comment: the date has been correcte
A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT_4
We discuss several aspects of superconformal field theories in four
dimensions (CFT_4), in the context of electric-magnetic duality. We analyse the
behaviour of anomalous currents under RG flow to a conformal fixed point in
N=1, D=4 supersymmetric gauge theories. We prove that the anomalous dimension
of the Konishi current is related to the slope of the beta function at the
critical point. We extend the duality map to the (nonchiral) Konishi current.
As a byproduct we compute the slope of the beta function in the strong coupling
regime. We note that the OPE of with itself does not close, but
mixes with a special additional operator which in general is the
Konishi current. We discuss the implications of this fact in generic
interacting conformal theories. In particular, a SCFT_4 seems to be naturally
equipped with a privileged off-critical deformation and this allows us
to argue that electric-magnetic duality can be extended to a neighborhood of
the critical point. We also stress that in SCFT_4 there are two central
charges, c and c', associated with the stress tensor and ,
respectively; c and c' allow us to count both the vector multiplet and the
matter multiplet effective degrees of freedom of the theory.Comment: harvmac tex, 28 pages, 3 figures. Version to be published in Nucl.
Phys.
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