65,918 research outputs found
Event shapes in N=4 super-Yang-Mills theory
We study event shapes in N=4 SYM describing the angular distribution of
energy and R-charge in the final states created by the simplest half-BPS scalar
operator. Applying the approach developed in the companion paper
arXiv:1309.0769, we compute these observables using the correlation functions
of certain components of the N=4 stress-tensor supermultiplet: the half-BPS
operator itself, the R-symmetry current and the stress tensor. We present
master formulas for the all-order event shapes as convolutions of the Mellin
amplitude defining the correlation function of the half-BPS operators, with a
coupling-independent kernel determined by the choice of the observable. We find
remarkably simple relations between various event shapes following from N=4
superconformal symmetry. We perform thorough checks at leading order in the
weak coupling expansion and show perfect agreement with the conventional
calculations based on amplitude techniques. We extend our results to strong
coupling using the correlation function of half-BPS operators obtained from the
AdS/CFT correspondence.Comment: 52 pages, 6 figures; v2: typos correcte
A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
Recent lattice data have reported an infrared suppressed, positivity
violating gluon propagator which is nonvanishing at zero momentum and a ghost
propagator which is no longer enhanced. This paper discusses how to obtain
analytical results which are in qualitative agreement with these lattice data
within the Gribov-Zwanziger framework. This framework allows one to take into
account effects related to the existence of gauge copies, by restricting the
domain of integration in the path integral to the Gribov region. We elaborate
to great extent on a previous short paper by presenting additional results,
also confirmed by the numerical simulations. A detailed discussion on the soft
breaking of the BRST symmetry arising in the Gribov-Zwanziger approach is
provided.Comment: 38 pages, 9 figures, the content of section V has been extended and
adapte
Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
We consider the singular behaviour of QCD scattering amplitudes in
kinematical configurations where two or more momenta of the external partons
become collinear. At the tree level, this behaviour is known to be controlled
by factorization formulae in which the singular collinear factor is universal
(process independent). We show that this strict (process-independent)
factorization is not valid at one-loop and higher-loop orders in the case of
the collinear limit in space-like regions (e.g., collinear radiation from
initial-state partons). We introduce a generalized version of all-order
collinear factorization, in which the space-like singular factors retain some
dependence on the momentum and colour charge of the non-collinear partons. We
present explicit results on one-loop and two-loop amplitudes for both the
two-parton and multiparton collinear limits. At the level of square amplitudes
and, more generally, cross sections in hadron--hadron collisions, the violation
of strict collinear factorization has implications on the non-abelian structure
of logarithmically-enhanced terms in perturbative calculations (starting from
the next-to-next-to-leading order) and on various factorization issues of mass
singularities (starting from the next-to-next-to-next-to-leading order).Comment: 81 pages, 5 figures, typos corrected in the text, few comments added
and inclusion of NOTE ADDED on recent development
BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
A connection between the gauge fixed dynamics of protected operators in
superconformal Yang-Mills theory in four dimensions and Calogero systems is
established. This connection generalizes the free Fermion description of the
chiral primary operators of the gauge theory formed out of a single complex
scalar to more general operators. In particular, a detailed analysis of
protected operators charged under an su(1|1)contained in psu(2,2|4) is carried
out and a class of operators is identified, whose dynamics is described by the
rational super-Calogero model. These results are generalized to arbitrary BPS
operators charged under an su(2|3) of the superconformal algebra. Analysis of
the non-local symmetries of the super-Calogero model is also carried out, and
it is shown that symmetry for a large class of protected operators is a
contraction of the corresponding Yangian algebra to a loop algebra.Comment: 29 pages, 3 figure
The Volume Operator in Spherically Symmetric Quantum Geometry
The spherically symmetric volume operator is discussed and all its
eigenstates and eigenvalues are computed. Even though the operator is more
complicated than its homogeneous analog, the spectra are related in the sense
that the larger spherically symmetric volume spectrum adds fine structure to
the homogeneous spectrum. The formulas of this paper complete the derivation of
an explicit calculus for spherically symmetric models which is needed for
future physical investigations.Comment: 25 pages, 2 figure
A generalized Hamiltonian Constraint Operator in Loop Quantum Gravity and its simplest Euclidean Matrix Elements
We study a generalized version of the Hamiltonian constraint operator in
nonperturbative loop quantum gravity. The generalization is based on admitting
arbitrary irreducible SU(2) representations in the regularization of the
operator, in contrast to the original definition where only the fundamental
representation is taken. This leads to a quantization ambiguity and to a family
of operators with the same classical limit. We calculate the action of the
Euclidean part of the generalized Hamiltonian constraint on trivalent states,
using the graphical notation of Temperley-Lieb recoupling theory. We discuss
the relation between this generalization of the Hamiltonian constraint and
crossing symmetry.Comment: 35 pp, 20 eps figures; minor corrections, references added; version
to appear in Class. Quant. Gra
Quantum Holonomy in Three-dimensional General Covariant Field Theory and Link Invariant
We consider quantum holonomy of some three-dimensional general covariant
non-Abelian field theory in Landau gauge and confirm a previous result
partially proven. We show that quantum holonomy retains metric independence
after explicit gauge fixing and hence possesses the topological property of a
link invariant. We examine the generalized quantum holonomy defined on a
multi-component link and discuss its relation to a polynomial for the link.Comment: RevTex, 12 pages. The metric independence of path integral measure is
justified and the case of multi-component link is discussed in detail. To be
published in Physical Review
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