3,787 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
Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
This paper studies giant magnons in AdS_4 x CP^3 using both the string
sigma-model and the algebraic curve. We complete the dictionary of solutions by
finding the dyonic generalisation of the CP^1 string solution, which matches
the `small' giant magnon in the algebraic curve, and by pointing out that the
solution recently constructed by the dressing method is the `big' giant magnon.
We then use the curve to compute finite-J corrections to all cases, which for
the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we
recover the S^5 answer, but for the `small' and `big' giant magnons we obtain
new corrections.Comment: 22 pages, 3 figures, 2 tables. v2 adds note on breather solution, and
minor clarification
Energy Disaggregation via Adaptive Filtering
The energy disaggregation problem is recovering device level power
consumption signals from the aggregate power consumption signal for a building.
We show in this paper how the disaggregation problem can be reformulated as an
adaptive filtering problem. This gives both a novel disaggregation algorithm
and a better theoretical understanding for disaggregation. In particular, we
show how the disaggregation problem can be solved online using a filter bank
and discuss its optimality.Comment: Submitted to 51st Annual Allerton Conference on Communication,
Control, and Computin
Blind Identification via Lifting
Blind system identification is known to be an ill-posed problem and without
further assumptions, no unique solution is at hand. In this contribution, we
are concerned with the task of identifying an ARX model from only output
measurements. We phrase this as a constrained rank minimization problem and
present a relaxed convex formulation to approximate its solution. To make the
problem well posed we assume that the sought input lies in some known linear
subspace.Comment: Submitted to the IFAC World Congress 2014. arXiv admin note: text
overlap with arXiv:1303.671
Stream Sampling for Frequency Cap Statistics
Unaggregated data, in streamed or distributed form, is prevalent and come
from diverse application domains which include interactions of users with web
services and IP traffic. Data elements have {\em keys} (cookies, users,
queries) and elements with different keys interleave. Analytics on such data
typically utilizes statistics stated in terms of the frequencies of keys. The
two most common statistics are {\em distinct}, which is the number of active
keys in a specified segment, and {\em sum}, which is the sum of the frequencies
of keys in the segment. Both are special cases of {\em cap} statistics, defined
as the sum of frequencies {\em capped} by a parameter , which are popular in
online advertising platforms. Aggregation by key, however, is costly, requiring
state proportional to the number of distinct keys, and therefore we are
interested in estimating these statistics or more generally, sampling the data,
without aggregation. We present a sampling framework for unaggregated data that
uses a single pass (for streams) or two passes (for distributed data) and state
proportional to the desired sample size. Our design provides the first
effective solution for general frequency cap statistics. Our -capped
samples provide estimates with tight statistical guarantees for cap statistics
with and nonnegative unbiased estimates of {\em any} monotone
non-decreasing frequency statistics. An added benefit of our unified design is
facilitating {\em multi-objective samples}, which provide estimates with
statistical guarantees for a specified set of different statistics, using a
single, smaller sample.Comment: 21 pages, 4 figures, preliminary version will appear in KDD 201
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
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