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 $W_{\wedge}$, 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

New Ambitwistor String Theories

We describe new ambitwistor string theories that give rise to the recent amplitude formulae for Einstein-Yang-Mills, (Dirac)-Born-Infeld, Galileons and others introduced by Cachazo, He and Yuan. In the case of the Einstein-Yang-Mills amplitudes, an important role is played by a novel worldsheet conformal field theory that provides the appropriate colour factors precisely without the spurious multitrace terms of earlier models that had to be ignored by hand. This is needed to obtain the correct multitrace terms that arise when Yang-Mills is coupled to gravity.Comment: 34 pages, 2 figures, 5 tables. v2: minor changes, published versio