3,955 research outputs found
Magnon dispersion to four loops in the ABJM and ABJ models
The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry
which is believed to be integrable in the planar limit. However, there is a
coupling dependent function that appears in the magnon dispersion relation and
the asymptotic Bethe ansatz that is only known to leading order at strong and
weak coupling. We compute this function to four loops in perturbation theory by
an explicit Feynman diagram calculation for both the ABJM model and the ABJ
extension. We find that all coefficients have maximal transcendentality. We
then compute the four-loop wrapping correction for a scalar operator in the 20
of SU(4) and find that it agrees with a recent prediction from the ABJM
Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ
model that might be perturbatively integrable at all loop orders but has a
short range Hamiltonian.Comment: LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram
corrected: modified result in the ABJ case only, formulations improved, typos
fixed, references added; v3: signs of three diagrams corrected, modifying the
final resul
Robust Subspace System Identification via Weighted Nuclear Norm Optimization
Subspace identification is a classical and very well studied problem in
system identification. The problem was recently posed as a convex optimization
problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this
framework to handle outliers. The proposed framework takes the form of a convex
optimization problem with an objective that trades off fit, rank and sparsity.
As in robust PCA, it can be problematic to find a suitable regularization
parameter. We show how the space in which a suitable parameter should be sought
can be limited to a bounded open set of the two dimensional parameter space. In
practice, this is very useful since it restricts the parameter space that is
needed to be surveyed.Comment: Submitted to the IFAC World Congress 201
Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
Using N=2 superspace techniques we compute the four-loop spectrum of single
trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric
Chern-Simons theories. Our computation yields a four-loop contribution to the
function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion
relation which has fixed maximum transcendentality and coincides with the
findings in components given in the revised versions of arXiv:0908.2463 and
arXiv:0912.3460. We also discuss possible scenarios for an all-loop function
h^2(\lambda) that interpolates between weak and strong couplings.Comment: LaTeX, feynmp, 34 pages; v2: typos corrected, formulations improved,
references adde
Finite energy shifts in SU(n) supersymmetric Yang-Mills theory on T^3xR at weak coupling
We consider a semi-classical treatment, in the regime of weak gauge coupling,
of supersymmetric Yang-Mills theory in a space-time of the form T^3xR with
SU(n)/Z_n gauge group and a non-trivial gauge bundle. More specifically, we
consider the theories obtained as power series expansions around a certain
class of normalizable vacua of the classical theory, corresponding to isolated
points in the moduli space of flat connections, and the perturbative
corrections to the free energy eigenstates and eigenvalues in the weakly
interacting theory. The perturbation theory construction of the interacting
Hilbert space is complicated by the divergence of the norm of the interacting
states. Consequently, the free and interacting Hilbert furnish unitarily
inequivalent representation of the algebra of creation and annihilation
operators of the quantum theory. We discuss a consistent redefinition of the
Hilbert space norm to obtain the interacting Hilbert space and the properties
of the interacting representation. In particular, we consider the lowest
non-vanishing corrections to the free energy spectrum and discuss the crucial
importance of supersymmetry for these corrections to be finite.Comment: 31 pages, 1 figure, v4 Minor changes, references correcte
Signatures from an extra-dimensional seesaw model
We study the generation of small neutrino masses in an extra-dimensional
model, where right-handed neutrinos are allowed to propagate in the extra
dimension, while the Standard Model particles are confined to a brane.
Motivated by the fact that extra-dimensional models are non-renormalizable, we
truncate the Kaluza-Klein towers at a maximal extra-dimensional momentum. The
structure of the bulk Majorana mass term, motivated by the Sherk-Schwarz
mechanism, implies that the right-handed Kaluza-Klein neutrinos pair to form
Dirac neutrinos, except for a number of unpaired Majorana neutrinos at the top
of each tower. These heavy Majorana neutrinos are the only sources of lepton
number breaking in the model, and similarly to the type-I seesaw mechanism,
they naturally generate small masses for the left-handed neutrinos. The lower
Kaluza-Klein modes mix with the light neutrinos, and the mixing effects are not
suppressed with respect to the light-neutrino masses. Compared to conventional
fermionic seesaw models, such mixing can be more significant. We study the
signals of this model at the Large Hadron Collider, and find that the current
low-energy bounds on the non-unitarity of the leptonic mixing matrix are strong
enough to exclude an observation.Comment: 17 pages, 3 figures, REVTeX4. Final version published in Phys. Rev.
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