Welcome

Double copy reversed: a multi-Regge example

• Johannes Brödel

Most double-copies have been identified starting from the gauge-theory side. Here, I am going to discuss the opposite direction and ask the question: what does a theory need to be decomposable into two copies of a different theory? While this question will have to remain unanswered to some extent, I will consider the multi-Regge limit in N=4 super-Yang-Mills theory and show, how the associated remainder function can be reformulated as a double-copy.

Colour-Kinematics Duality and the Double Copy: A Lagrangian and Homotopy Algebraic Perspective

• Leron Borsten

We shall review recent work on when, how and in what sense colour-kinematics duality and the double copy can be realised at the level of off-shell fields and Lagrangians. In the case of pure Yang–Mills theory we argue that colour-kinematics duality can be made manifest in the Batalin–Vilkovisky action, but only up to Jacobian counterterms that must enter at the loop level. The latter implies a departure from what is normally understood by colour-kinematics duality in that the counterterms will generically break it. However, this notion of CK duality is quite natural, as a symmetry of the action itself, and implies the validity of the double copy. We then describe the generalisation to super Yang–Mills theory, where Sen’s formalism for self-dual field strengths emerges automatically. We conclude by discussing the mathematical underpinnings of these observations in terms of homotopy algebras, where Chern–Simons theory provides the paradigmatic example. Figuratively, colour–kinematics duality is a symmetry of Yang–Mills theory in the same sense that a mug is a donut.

Perturbative quantum field theory, colour-kinematics duality and homotopy algebras

• Christian Saemann

I review the description of perturbative quantum field theory in terms of homotopy algebras, which provides a unifying picture for actions and scattering amplitudes. In this picture, each field theory is encoded in an L∞-algebra, a generalization of a differential graded Lie algebra, and any extra structure on scattering amplitudes amounts to a homotopy algebraic refinement of the L∞-algebra. I discuss in detail the case colour-kinematics duality, where the refinement is captured by a generalization of homotopy BV-algebras. This perspective is well-motivated from string theory and also yields an explicit description of the double copy. It provides a clean mathematical characterization of colour-kinematics duality and identifies the kinematical algebra for any CK-dual field theory.

Inverting Berends-Giele in search of BCJ numerators and stringy recursion relations

• Hadleigh Frost

The Berends-Giele recursion relations give a rapid way to compute gauge theory amplitudes at tree level. We show how to invert the the Berends-Giele relation, and how this implies BCJ and KLT. These results imply identities among the functions that arise in CHY-like formulas, with applications to computing gauge theory amplitudes and also string correlators.

Color-Dual Effective Field Theory

• J. J. Carrasco

Pairs of color-dual numerators can be composed to generate new color-dual numerators. This presents an opportunity to efficiently climb to amplitudes of arbitrarily high mass dimension, without resorting to ever more expensive Ansätze, thereby spanning the tower of double-copy consistent gauge and gravity operators with a small number of building blocks. I will apply this technology towards learning some lessons about the color-dual fate of N=4 supergravity.

Recent Progress on the Kinematic Algebra

• Henrik Johansson

This talk will review the problem of finding kinematic algebras that generate BCJ numerators, and will highlight some of the recent progress and explicit constructions.

Pure spinor field-theory description of 10D super-Yang-Mills and Color-Kinematics Duality

• Max Guillen

In this talk I will first review the basic ingredients which allow one to formulate 10D super-Yang-Mills on pure spinor superspace. The respective pure spinor master action in the gauge b₀V=QΞ, will then be used to show that tree-level scattering amplitudes calculated via perturbiner methods, match those obtained from pure spinor CFT techniques. I will also discuss how to compute pure spinor kinematic numerators through the use of standard Feynman rules, and show that these are described by compact expressions involving the b-ghost operator. Remarkably, color-kinematics duality will be shown to immediately emerge after imposing the Siegel gauge condition b₀V = 0.

The Seeds of EFT Double Copy

• Jasper Roosmale Nepveu

There are currently two approaches that generalize the double copy in the context of effective field theories. One method is based on the color-kinematics duality and considers color-dual numerators that depend on both color and kinematics. The other method follows the Kawai-Lewellen-Tye (KLT) double copy, taking KLT kernels with higher-derivative corrections. In this talk, I will gain insight in these approaches and bridge them together by constructing functions of both color and kinematics that have the same functional form as traces of color-group generators.

Gravity solutions via twistor theory

• Silvia Nagy

I will show how the double copy for classical solutions can be aided by an unexpected connection with twistor theory - this provides an explanation for the formulae found in spacetime, and also allows us to expand the space of solutions. I will also touch upon future directions, building on insights from the self-dual sector.

The Newman-Penrose Map and the Classical Double Copy

• Kara Farnsworth

In this talk I will discuss the Newman-Penrose map, which relates a class of exact solutions of Einstein’s equations to self-dual solutions of Maxwell's equations. This map, although not technically a double copy, produces similar results to other formulations of the classical double copy and applies to a general class of spacetimes. I will present several examples of spacetimes related to gauge theories under the Newman-Penrose map and compare with other formulations, including upcoming work in maximally symmetric backgrounds.

Double-copy and unitarity of tree-level string amplitudes

• Sebastian Mizera

String theory amplitudes at tree level respect double-copy factorization at every massive resonance. We use this fact to study unitarity of string theory on-shell and prove it in space-time dimensions up to 6.

Twistor amplitudes and CK duality

• Alfredo Guevara González

TBA

Geometry-kinematics duality and soft theorems

• Julio Parra-Martínez

In this talk I will explain a geometric picture that relates all tree-level scattering amplitudes of massless bosons and provides a unified framework for old and new soft theorems.

Double Copying Exceptional Field Theories

• David Berman

We examine exceptional field theory through the lens of a generalised double copy formalism. This allows us to construct classical solutions in M-theory using a Kerr-Schild type ansatz and along the way indicates hints towards a single copy of M-theory. https://inspirehep.net/literature/2018014

A Topologically Massive Double Copy

• Nathan Moynihan

I will discuss various aspects of the double copy in 2+1 dimensional topologically massive gauge/gravity theories.

Massive Color-Kinematics Duality and Well-Defined Double Copies

• Mariana Carrillo González

In this talk, I will give a short review on the color-kinematics duality for theories with massive mediators and the issues arising when constructing a double copy. I will focus on two different alternatives that can avoid spurious poles. The first one requires a specific spectrum of masses in the theory and the second uses special kinematics in 3 dimensions. First, I will show how a cubic scalar theory with a special mass spectrum and tuned cubic vertices can give rise to a well-defined double copy. Afterwards, I will focus on the 3d case and explain different double copy constructions for topologically massive theories.

Worldsheet description of Kerr interactions

• Alexander Ochirov

The recent progress of applying QFT methods to classical GR has provided a new perspective on the Kerr black hole solution. Its leading gravitational interactions are known to involve an infinite tower of spin-induced multipoles with unit coupling constants. In this talk, I will present a novel form of the classical worldline action that implements these multipole interactions within a single worldsheet integral, which is inspired by the Newman-Janis shift relationship of the Kerr and Schwarzschild solutions. I will also discuss connections to our recently discovered ability to model such interactions using a certain family of scattering amplitudes, as well as a simple double-copy property hidden within.

Maximally Supersymmetric Massive Gravity and the Double-Copy

• Callum Jones

In this talk I will describe the construction of supersymmetrizations of a special class of models with massive spin-2 "gravitons" in d=4. Using various pieces of on-shell technology, including massive on-shell superspace and the double-copy, I will argue that there exists a unique "simplest" model of massive gravity with N=4 supersymmetry and maximal R-symmetry. This model has no free parameters in the dRGT potential and yet is (possibly uniquely) consistent with known UV constraints from superluminality, analyticity and unitarity. I will also describe the prospect of constructing this model as a double-copy of N=2 supersymmetric massive Yang-Mills and the various difficulties associated with a massive double-copy.

Bootstrapping the KLT Formula

• Shruti Paranjape

The tree-level double copy is the field theory limit of the string theory KLT relations. In this limit, two features of the KLT relations are lost - higher derivative corrections and massive states. In this talk, we will focus on the former and develop a bootstrap procedure based on locality of the double-copy amplitudes. This will allow us to generalize the field theory double copy to include effective field theories and theories with mass, via manipulations of the KLT kernel.

The double copy and gravitational waves

• Zvi Bern

Closing