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

The local convexity of solving systems of quadratic equations

This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a variety of applications, including covariance sketching of high-dimensional data streams, quadratic regression, quantum state tomography, among others. A natural approach to this problem is to minimize the loss function $f(U) = \sum_i (y_i - a_i^TUU^Ta_i)^2$ which has an entire manifold of solutions given by $\{XO\}_{O\in\mathcal{O}_r}$ where $\mathcal{O}_r$ is the orthogonal group of $r\times r$ orthogonal matrices; this is {\it non-convex} in the $n\times r$ matrix $U$, but methods like gradient descent are simple and easy to implement (as compared to semidefinite relaxation approaches). In this paper we show that once we have $m \geq C nr \log^2(n)$ samples from isotropic gaussian $a_i$, with high probability {\em (a)} this function admits a dimension-independent region of {\em local strong convexity} on lines perpendicular to the solution manifold, and {\em (b)} with an additional polynomial factor of $r$ samples, a simple spectral initialization will land within the region of convexity with high probability. Together, this implies that gradient descent with initialization (but no re-sampling) will converge linearly to the correct $X$, up to an orthogonal transformation. We believe that this general technique (local convexity reachable by spectral initialization) should prove applicable to a broader class of nonconvex optimization problems.Comment: 36 pages, 3 figure

Law of refraction for generalised confocal lenslet arrays

We derive the law of generalised refraction for generalised confocal lenslet arrays, which are arrays of misaligned telescopes. We have implemented this law of refraction in TIM, a custom open-source ray tracer.Comment: 4 pages, 3 figure

Web matrices : structural properties and generating combinatorial identities

In this paper we present new results for the combinatorics of web diagrams and web worlds. These are discrete objects that arise in the physics of calculating scattering amplitudes in non-abelian gauge theories. Web-colouring and web-mixing matrices (collectively known as web matrices) are indexed by ordered pairs of web-diagrams and contain information relating the number of colourings of the first web diagram that will produce the second diagram. We introduce the black diamond product on power series and show how it determines the web-colouring matrix of disjoint web worlds. Furthermore, we show that combining known physical results with the black diamond product gives a new technique for generating combinatorial identities. Due to the complicated action of the product on power series, the resulting identities appear highly non-trivial. We present two results to explain repeated entries that appear in the web matrices. The first of these shows how diagonal web matrix entries will be the same if the comparability graphs of their associated decomposition posets are the same. The second result concerns general repeated entries in conjunction with a flipping operation on web diagrams. We present a combinatorial proof of idempotency of the web-mixing matrices, previously established using physical arguments only. We also show how the entries of the square of the web-colouring matrix can be achieved by a linear transformation that maps the standard basis for formal power series in one variable to a sequence of polynomials. We look at one parameterized web world that is related to indecomposable permutations and show how determining the web-colouring matrix entries in this case is equivalent to a combinatorics on words problem

The MC@NLO 4.0 Event Generator

This is the user's manual of MC@NLO 4.0. This package is a practical implementation, based upon the Fortran HERWIG and Herwig++ event generators, of the MC@NLO formalism, which allows one to incorporate NLO QCD matrix elements consistently into a parton shower framework. Processes available in this version include the hadroproduction of single vector and Higgs bosons, vector boson pairs, heavy quark pairs, single top, single top in association with a W, single top in association with a charged Higgs in type I or II 2HDM models, lepton pairs, and Higgs bosons in association with a W or Z. Spin correlations are included for all processes except ZZ production. This document is self-contained, but we emphasise the main differences with respect to previous versions.Comment: 36 pages, no figure

Top polarisation studies in H−tH^-t and WtWt production

The polarisation of top quarks produced in high energy processes can be a very sensitive probe of physics beyond the Standard Model. The kinematical distributions of the decay products of the top quark can provide clean information on the polarisation of the produced top and thus can probe new physics effects in the top quark sector. We study some of the recently proposed polarisation observables involving the decay products of the top quark in the context of $H^-t$ and $Wt$ production. We show that the effect of the top polarisation on the decay lepton azimuthal angle distribution, studied recently for these processes at leading order in QCD, is robust with respect to the inclusion of next-to-leading order and parton shower corrections. We also consider the leptonic polar angle, as well as recently proposed energy-related distributions of the top decay products. We construct asymmetry parameters from these observables, which can be used to distinguish the new physics signal from the $Wt$ background and discriminate between different values of $\tan\beta$ and $m_{H^-}$ in a general type II two-Higgs doublet model. Finally, we show that similar observables may be useful in separating a Standard Model $Wt$ signal from the much larger QCD induced top pair production background.Comment: 33 pages, 35 figures, references adde

A global fit of top quark effective theory to data

In this paper we present a global fit of beyond the Standard Model (BSM) dimension six operators relevant to the top quark sector to currently available data. Experimental measurements include parton-level top-pair and single top production from the LHC and the Tevatron. Higher order QCD corrections are modelled using differential and global K-factors, and we use novel fast-fitting techniques developed in the context of Monte Carlo event generator tuning to perform the fit. This allows us to provide new, fully correlated and model-independent bounds on new physics effects in the top sector from the most current direct hadron-collider measurements in light of the involved theoretical and experimental systematics. As a by-product, our analysis constitutes a proof-of-principle that fast fitting of theory to data is possible in the top quark sector, and paves the way for a more detailed analysis including top quark decays, detector corrections and precision observables.Comment: Additional references and preprint code added. Minor error in generation of plots fixed, no conclusions affecte

Ejection of Supernova-Enriched Gas From Dwarf Disk Galaxies

We examine the efficiency with which supernova-enriched gas may be ejected from dwarf disk galaxies, using a methodology previously employed to study the self-enrichment efficiency of dwarf spheroidal systems. Unlike previous studies that focused on highly concentrated starbursts, in the current work we consider discrete supernova events spread throughout various fractions of the disk. We model disk systems having gas masses of 10^8 and 10^9 solar masses with supernova rates of 30, 300, and 3000 per Myr. The supernova events are confined to the midplane of the disk, but distributed over radii of 0, 30, and 80% of the disk radius, consistent with expectations for Type II supernovae. In agreement with earlier studies, we find that the enriched material from supernovae is largely lost when the supernovae are concentrated near the nucleus, as expected for a starburst event. In contrast, however, we find the loss of enriched material to be much less efficient when the supernovae occur over even a relatively small fraction of the disk. The difference is due to the ability of the system to relax following supernova events that occur over more extended regions. Larger physical separations also reduce the likelihood of supernovae going off within low-density "chimneys" swept out by previous supernovae. We also find that, for the most distributed systems, significant metal loss is more likely to be accompanied by significant mass loss. A comparison with theoretical predications indicates that, when undergoing self-regulated star formation, galaxies in the mass range considered shall efficiently retain the products of Type II supernovae.Comment: 16 pages, 14 figures, to appear in Astrophysical Journal; higher resolution figures available through Ap