552 research outputs found
Chow groups of weighted hypersurfaces
We extend a result of to Esnault-Levine-Viehweg concerning the Chow groups of
hypersurfaces in projective space to those in weighted projective spaces
On the ABJM four-point amplitude at three loops and BDS exponentiation
We study the three-loop four-point amplitude in ABJM theory. We determine the
dual conformal invariant integrals with highest number of propagators and fix
their coefficients by two-particle cuts. Evaluating such a combination of
integrals in dimensional regularization we provide evidence for exponentiation
of the amplitude, including the finite terms. In addition we show that the
three-loop amplitude can be expressed in terms of classical polylogarithms of
uniform degree of transcendentality.Comment: 31 pages, 4 figure
Minimal two-sphere model of the generation of fluid flow at low Reynolds numbers
Locomotion and generation of flow at low Reynolds number are subject to
severe limitations due to the irrelevance of inertia: the "scallop theorem"
requires that the system have at least two degrees of freedom, which move in
non-reciprocal fashion, i.e. breaking time-reversal symmetry. We show here that
a minimal model consisting of just two spheres driven by harmonic potentials is
capable of generating flow. In this pump system the two degrees of freedom are
the mean and relative positions of the two spheres. We have performed and
compared analytical predictions, numerical simulation and experiments, showing
that a time-reversible drive is sufficient to induce flow.Comment: 5 pages, 3 figures, revised version, corrected typo
Dynamics for Systems of Screw Dislocations
The goal of this paper is the analytical validation of a model of Cermelli
and Gurtin for an evolution law for systems of screw dislocations under the
assumption of antiplane shear. The motion of the dislocations is restricted to
a discrete set of glide directions, which are properties of the material. The
evolution law is given by a "maximal dissipation criterion", leading to a
system of differential inclusions. Short time existence, uniqueness,
cross-slip, and fine cross-slip of solutions are proved.Comment: 35 pages, 5 figure
Light-like Wilson loops in ABJM and maximal transcendentality
We revisit the computation of the two-loop light-like tetragonal Wilson loop
for three dimensional pure Chern-Simons and N=6 Chern-Simons-matter theory,
within dimensional regularization with dimensional reduction scheme. Our
examination shows that, contrary to prior belief, the result respects maximal
transcendentality as is the case of the four-point scattering amplitude of the
theory. Remarkably, the corrected result matches exactly the scattering
amplitude both in the divergent and in the finite parts, constants included.Comment: 11 page
The 1/2 BPS Wilson loop in ABJ(M) at two loops: The details
We compute the expectation value of the 1/2 BPS circular Wilson loop operator
in ABJ(M) theory at two loops in perturbation theory. Our result turns out to
be in exact agreement with the weak coupling limit of the prediction coming
from localization, including finite N contributions associated to non-planar
diagrams. It also confirms the identification of the correct framing factor
that connects framing-zero and framing-one expressions, previously proposed.
The evaluation of the 1/2 BPS operator is made technically difficult in
comparison with other observables of ABJ(M) theory by the appearance of
integrals involving the coupling between fermions and gauge fields, which are
absent for instance in the 1/6 BPS case. We describe in detail how to
analytically solve these integrals in dimensional regularization with
dimensional reduction (DRED). By suitably performing the physical limit to
three dimensions we clarify the role played by short distance divergences on
the final result and the mechanism of their cancellation.Comment: 54 pages, 2 figure
BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
We study a family of circular BPS Wilson loops in N=6 super
Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar
and fermionic couplings depend on two deformation parameters and these
operators can be considered as the ABJ(M) counterpart of the DGRT latitudes
defined in N=4 SYM. We perform a complete two-loop analysis of their vacuum
expectation value, discuss the framing dependence and propose a general
relation with cohomologically equivalent bosonic operators. We make an all-loop
proposal for computing the Bremsstrahlung function associated to the 1/2-BPS
cusp in terms of these generalized Wilson loops. When applied to our two-loop
result it reproduces the known expression. Finally, we comment on the
generalization of this proposal to the bosonic 1/6-BPS case.Comment: 46 pages, 6 figures; references adde
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