2,834 research outputs found
The Kinematic Algebras from the Scattering Equations
We study kinematic algebras associated to the recently proposed scattering
equations, which arise in the description of the scattering of massless
particles. In particular, we describe the role that these algebras play in the
BCJ duality between colour and kinematics in gauge theory, and its relation to
gravity. We find that the scattering equations are a consistency condition for
a self-dual-type vertex which is associated to each solution of those
equations. We also identify an extension of the anti-self-dual vertex, such
that the two vertices are not conjugate in general. Both vertices correspond to
the structure constants of Lie algebras. We give a prescription for the use of
the generators of these Lie algebras in trivalent graphs that leads to a
natural set of BCJ numerators. In particular, we write BCJ numerators for each
contribution to the amplitude associated to a solution of the scattering
equations. This leads to a decomposition of the determinant of a certain
kinematic matrix, which appears naturally in the amplitudes, in terms of
trivalent graphs. We also present the kinematic analogues of colour traces,
according to these algebras, and the associated decomposition of that
determinant.Comment: 23 pages, 4 figure
Enriching Information to Prevent Bank Runs
Sequential service in the banking sector, as modeled by Diamondand Dybvig (1983), is a barrier to full insurance and potential source offinancial fragility against which deposit insurance is infeasible (Wallace,1988). In this paper, we pursue a different perspective, viewingthe sequence of contacts as opportunities to extract informationthrough a larger message space with commitment to richer promises.As we show, if preferences satisfy a separating property then the desiredelimination of dominated strategies (Green and Lin, 2003) occurseven when shocks are correlated. In this manner the sequential servicepromotes stability.
The Tenure Game: Building Up Academic Habits
Why do some academics continue to be productive after receiving tenure? This paper answers this question by using a Stackelberg differential game between departments and scholars. We show that departments can set tenure rules and standards as incentives for scholars to accumulate academic habits. As a result, academic habits have a lasting positive impact in scholar’s productivity, leading to higher scholar’s productivity rate of growth and higher productivity level.Role of economists; sociology of economics.
Black holes and the double copy
Recently, a perturbative duality between gauge and gravity theories (the
double copy) has been discovered, that is believed to hold to all loop orders.
In this paper, we examine the relationship between classical solutions of
non-Abelian gauge theory and gravity. We propose a general class of gauge
theory solutions that double copy to gravity, namely those involving stationary
Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their
higher-dimensional equivalents) emerge as special cases. We also discuss plane
wave solutions. Furthermore, a recently examined double copy between the
self-dual sectors of Yang-Mills theory and gravity can be reinterpreted using a
momentum-space generalisation of the Kerr-Schild framework.Comment: 22 pages; typos corrected and references adde
From Moyal deformations to chiral higher-spin theories and to celestial algebras
We study the connection of Moyal deformations of self-dual gravity and
self-dual Yang-Mills theory to chiral higher-spin theories, and also to
deformations of operator algebras in celestial holography. The relation to
Moyal deformations illuminates various aspects of the structure of chiral
higher-spin theories. For instance, the appearance of the self-dual kinematic
algebra in all the theories considered here leads via the double copy to
vanishing tree-level scattering amplitudes. Regarding celestial holography, the
Moyal deformation of self-dual gravity was recently shown to lead to the loop
algebra of , and we obtain here the analogous deformation of a
Kac-Moody algebra corresponding to Moyal-deformed self-dual Yang-Mills theory.
We also introduce the celestial algebras for various chiral higher-spin
theories.Comment: 30 pages, 3 figures; v2: minor change
Holographic Models for Theories with Hyperscaling Violation
We study in detail a variety of gravitational toy models for
hyperscaling-violating Lifshitz (hvLif) space-times. These space-times have
been recently explored as holographic dual models for condensed matter systems.
We start by considering a model of gravity coupled to a massive vector field
and a dilaton with a potential. This model supports the full class of hvLif
space-times and special attention is given to the particular values of the
scaling exponents appearing in certain non-Fermi liquids. We study linearized
perturbations in this model, and consider probe fields whose interactions mimic
those of the perturbations. The resulting equations of motion for the probe
fields are invariant under the Lifshitz scaling. We derive
Breitenlohner-Freedman-type bounds for these new probe fields. For the cases of
interest the hvLif space-times have curvature invariants that blow up in the
UV. We study the problem of constructing models in which the hvLif space-time
can have an AdS or Lifshitz UV completion. We also analyze reductions of
Schroedinger space-times and reductions of waves on extremal (intersecting)
branes, accompanied by transverse space reductions, that are solutions to
supergravity-like theories, exploring the allowed parameter range of the hvLif
scaling exponents.Comment: version 3: matches published versio
Colour-Kinematics Duality for One-Loop Rational Amplitudes
Colour-kinematics duality is the conjecture of a group theory-like structure
for the kinematic dependence of scattering amplitudes in gauge theory and
gravity. This structure has been verified at tree level in various ways, but
similar progress has been lacking at loop level, where the power of the duality
would be most significant. Here we explore colour-kinematics duality at one
loop using the self-dual sector as a starting point. The duality is shown to
exist in pure Yang-Mills theory for two infinite classes of amplitudes:
amplitudes with any number of particles either all of the same helicity or with
one particle helicity opposite the rest. We provide a simple Lagrangian-based
argument in favour of the double copy relation between gauge theory and gravity
amplitudes in these classes, and provide some explicit examples. We further
discuss aspects of the duality which persist after integration, leading to
relations among partial amplitudes. Finally, we describe form factors in the
self-dual theory at tree level which also satisfy the duality.Comment: 36 pages, 5 figures; v2: published versio
A note on convergence of Peck-Shell and Green-Lin mechanisms in the Diamond-Dybvig model
We study the e¤ects of population size in the Peck-Shell analysis ofbank runs. We nd that a contract featuring equal-treatment for al-most all depositors of the same type approximates the optimum. Becausethe approximation also satis es Green-Lin incentive constraints, when theplanner discloses positions in the queue, welfare in these alternative spec-i cations are sandwiched. Disclosure, however, is not needed since ourapproximating contract is not subject to runs.keywords: bank fragility, role of population size, role of aggregate uncer-tainty
Disparity compensation using geometric transforms
This dissertation describes the research and development of some techniques to enhance
the disparity compensation in 3D video compression algorithms. Disparity compensation
is usually performed using a block matching technique between views, disregarding the
various levels of disparity present for objects at different depths in the scene. An alternative
coding scheme is proposed, taking advantage of the cameras setup information and
the object’s depth in the scene, to compensate more complex spatial distortions, being
able to improve disparity compensation even with convergent cameras.
In order to perform a more accurate disparity compensation, the reference picture
list is enriched with additional geometrically transformed images, for the most relevant
object’s levels of depth in the scene, resulting from projections of one view to another.
This scheme can be implemented in any state-of-the-art video codec, as H.264/AVC or
HEVC, in order to improve the disparity matching accuracy between views.
Experimental results, using MV-HEVC extension, show the efficiency of the proposed
method for coding stereo video, presenting bitrate savings up to 2.87%, for convergent
camera sequences, and 1.52% for parallel camera sequences. Also a method to choose
the geometrically transformed inter view reference pictures was developed, in order to
reduce unnecessary overhead for unused reference pictures. By selecting and adding to
the reference picture list, only the most useful pictures, all results improved, presenting
bitrate savings up to 3.06% for convergent camera sequences, and 2% for parallel camera
sequences
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