4,433 research outputs found
On structure constants with two spinning twist-two operators
I consider three-point functions of one protected and two unprotected
twist-two operators with spin in N=4 SYM at weak coupling. At one loop I
formulate an empiric conjecture for the dependence of the corresponding
structure constants on the spins of the operators. Using such an ansatz and
some input from explicit perturbative results, I fix completely various
infinite sets of one-loop structure constants of these three-point functions.
Finally, I determine the two-loop corrections to the structure constants for a
few fixed values of the spins of the operators.Comment: 21 page
ABJM -Bremsstrahlung at four loops and beyond
In ABJ(M) theory a generalized cusp can be constructed out of the 1/6 BPS
Wilson line by introducing an angle in the spacial contour and/or an
angle in the internal R-symmetry space. The small angles limits of its
anomalous dimension are controlled by corresponding Bremsstrahlung functions.
In this note we compute the internal space -Bremsstrahlung function to
four loops at weak coupling in the planar limit. Based on this result, we
propose an all order conjecture for the -Bremsstrahlung function.Comment: 40 pages; v2: references added, JHEP published extended versio
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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