8,326 research outputs found
Hexagon OPE Resummation and Multi-Regge Kinematics
We analyse the OPE contribution of gluon bound states in the double scaling
limit of the hexagonal Wilson loop in planar N=4 super Yang-Mills theory. We
provide a systematic procedure for perturbatively resumming the contributions
from single-particle bound states of gluons and expressing the result order by
order in terms of two-variable polylogarithms. We also analyse certain
contributions from two-particle gluon bound states and find that, after
analytic continuation to the Mandelstam region and passing to
multi-Regge kinematics (MRK), only the single-particle gluon bound states
contribute. From this double-scaled version of MRK we are able to reconstruct
the full hexagon remainder function in MRK up to five loops by invoking
single-valuedness of the results.Comment: 29 pages, 3 figures, 4 ancillary file
Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary
The mathematical formalism necessary for the diagramatic evaluation of
quantum corrections to a conformally invariant field theory for a
self-interacting scalar field on a curved manifold with boundary is considered.
The evaluation of quantum corrections to the effective action past one-loop
necessitates diagramatic techniques. Diagramatic evaluations and higher
loop-order renormalisation can be best accomplished on a Riemannian manifold of
constant curvature accommodating a boundary of constant extrinsic curvature. In
such a context the stated evaluations can be accomplished through a consistent
interpretation of the Feynman rules within the spherical formulation of the
theory for which the method of images allows. To this effect, the mathematical
consequences of such an interpretation are analyzed and the spherical
formulation of the Feynman rules on the bounded manifold is, as a result,
developed.Comment: 12 pages, references added. To appear in Classical and Quantum
Gravit
Spin entanglement, decoherence and Bohm's EPR paradox
We obtain criteria for entanglement and the EPR paradox
for spin-entangled particles and analyse the effects of decoherence caused
by absorption and state purity errors. For a two qubit photonic state,
entanglement can occur for all transmission efficiencies. In this case,
the state preparation purity must be above a threshold value. However,
Bohm’s spin EPR paradox can be achieved only above a critical level of
loss. We calculate a required efficiency of 58%, which appears achievable
with current quantum optical technologies. For a macroscopic number of
particles prepared in a correlated state, spin entanglement and the EPR
paradox can be demonstrated using our criteria for efficiencies η > 1/3
and η > 2/3 respectively. This indicates a surprising insensitivity to loss
decoherence, in a macroscopic system of ultra-cold atoms or photons
Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate
Recent experimental measurements of atomic intensity correlations through
atom shot noise suggest that atomic quadrature phase correlations may soon be
measured with a similar precision. We propose a test of local realism with
mesoscopic numbers of massive particles based on such measurements. Using
dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic
atoms, we demonstrate that strongly entangled atomic beams may be produced
which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures,
in direct analogy to the position and momentum correlations originally
considered by EPR.Comment: Final published version (corrections in Ref. [32], updated
references
An action of the Polishchuk differential operator via punctured surfaces
For a family of Jacobians of smooth pointed curves there is a notion of tautological algebra. There is an action of on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to , on an algebra consisting of punctured Riemann surfaces. As an application we prove that a collection of tautological relations on moduli of curves, discovered by Faber and Zagier, come from a class of relations on the universal Jacobian
Naturally-phasematched second harmonic generation in a whispering gallery mode resonator
We demonstrate for the first time natural phase matching for optical
frequency doubling in a high-Q whispering gallery mode resonator made of
Lithium Niobate. A conversion efficiency of 9% is achieved at 30 micro Watt
in-coupled continuous wave pump power. The observed saturation pump power of
3.2 mW is almost two orders of magnitude lower than the state-of-the-art. This
suggests an application of our frequency doubler as a source of non-classical
light requiring only a low-power pump, which easily can be quantum noise
limited. Our theoretical analysis of the three-wave mixing in a whispering
gallery mode resonator provides the relative conversion efficiencies for
frequency doubling in various modes
Yangian symmetry of light-like Wilson loops
We show that a certain class of light-like Wilson loops exhibits a Yangian
symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops
we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills
theory in a certain kinematical regime. The fact that we find a Yangian
symmetry constraining their functional form can be thought of as the effect of
the original conformal symmetry associated to the scattering amplitudes in the
N=4 theory.Comment: 15 pages, 5 figure
On the Classification of Residues of the Grassmannian
We study leading singularities of scattering amplitudes which are obtained as
residues of an integral over a Grassmannian manifold. We recursively do the
transformation from twistors to momentum twistors and obtain an iterative
formula for Yangian invariants that involves a succession of dualized twistor
variables. This turns out to be useful in addressing the problem of classifying
the residues of the Grassmannian. The iterative formula leads naturally to new
coordinates on the Grassmannian in terms of which both composite and
non-composite residues appear on an equal footing. We write down residue
theorems in these new variables and classify the independent residues for some
simple examples. These variables also explicitly exhibit the distinct solutions
one expects to find for a given set of vanishing minors from Schubert calculus.Comment: 20 page
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently
been shown to transform covariantly with respect to a 'dual' superconformal
symmetry algebra, thus extending the conventional superconformal symmetry
algebra psu(2,2|4) of the theory. In this paper we derive the action of the
dual superconformal generators in on-shell superspace and extend the dual
generators suitably to leave scattering amplitudes invariant. We then study the
algebra of standard and dual symmetry generators and show that the inclusion of
the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a
Yangian. The non-local Yangian generators acting on amplitudes turn out to be
cyclically invariant due to special properties of psu(2,2|4). The
representation of the Yangian generators takes the same form as in the case of
local operators, suggesting that the Yangian symmetry is an intrinsic property
of planar N=4 super Yang-Mills, at least at tree level.Comment: 23 pages, no figures; v2: typos corrected, references added; v3:
minor changes, references adde
Magic identities for conformal four-point integrals
We propose an iterative procedure for constructing classes of off-shell
four-point conformal integrals which are identical. The proof of the identity
is based on the conformal properties of a subintegral common for the whole
class. The simplest example are the so-called `triple scalar box' and `tennis
court' integrals. In this case we also give an independent proof using the
method of Mellin--Barnes representation which can be applied in a similar way
for general off-shell Feynman integrals.Comment: 13 pages, 12 figures. New proof included with neater discussion of
contact terms. Typo correcte
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