YOUNGST@RS - Rebuilding the Tower of Babel: Bringing Together the Various Languages of Color-Kinematics Duality

11 Apr 2022, 14:00 → 13 Apr 2022, 20:20 Europe/Berlin

Mainz Institute for Theoretical Physics, Johannes Gutenberg University

The workshop has concluded. Recordings of the talks are available at MITP’s YouTube channel.

Since its inception in 2008, Bern–Carrasco–Johansson color–kinematics (CK) duality has been the source of many developments in quantum field theory and gravity. In its essence, CK duality states that the scattering amplitudes of a gauge theory can be reorganized to have the kinematic factors appearing in the integrand numerator mirror the same algebraic properties of the color factors. One of the most impressive consequences of this duality is the double copy prescription: substituting a copy of color factors of a gauge theory amplitude for CK‐compliant kinematic factors, one obtains scattering amplitudes for gravity scattering amplitudes: CK duality and the double copy prescription have been applied to a wide range of perturbative and non‐perturbative aspects of gauge theories and gravity. Many efforts have been made to extend this formalism to the study of classical solutions and to reformulate it at the off‐shell, Lagrangian level. CK duality and double copy have stimulated researchers to inquire into the very origin of these relations, unraveling rich mathematical structures such as homotopy algebras, and seeking for a geometric understanding of these relations through string theory, ambitwistor strings, and the scattering equations. The original formulation of this paradigm has been extended to encompass a growing zoo of double‐copy‐constructible theories, and it has been generalized to the case of loop amplitudes. The perspectives on the future of CK duality and double copy are encouraging, and range from the study of ultraviolet properties in supergravity to gravitational‐wave astronomy.

The diverse nature of the many contributions to this research field has given rise to many different languages and formalisms. The aim of this workshop is to bring together researchers active in the various incarnations and ramifications of CK duality and double copy in an inclusive and lively scientific environment. The purpose of this workshop is twofold: to allow researchers (especially the ones at the early stages of their career) to share and popularize their recent contributions to the field, and to find a common ground to set the goals the research community should pursue in the near term. The discovery of CK duality has changed the way we look at the fundamental theories underlying nature. Thirteen years later, this paradigm still remains vibrant and fruitful. While a fundamental all‐encompassing understanding of this feature of observed reality remains elusive, the quest to understand how the many features of this duality in various formalisms are interconnected will undoubtedly foster scientific advancement.

A list of the speakers is available here.

Monday 11 April

1 Welcome

2 Double copy reversed: a multi-Regge example

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.

Speaker: Johannes Brödel

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

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.

Speaker: Leron Borsten

Borsten_Youngstars_2022_Live.pdf

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

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.

Speaker: Christian Saemann

vortrag.pdf

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

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.

Speaker: Hadleigh Frost

6 Color-Dual Effective Field Theory

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.

Speaker: J. J. Carrasco

ColorDualEFT-MITP.pdf

7 Recent Progress on the Kinematic Algebra

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.

Speaker: Henrik Johansson

MITP_2022_Johansson.pdf

Tuesday 12 April

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

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.

Speaker: Max Guillen

Presentation-Mainz.pdf

9 The Seeds of EFT Double Copy

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.

Speaker: Jasper Roosmale Nepveu

Younstars_RoosmaleNepveu.pdf

10 Gravity solutions via twistor theory

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.

Speaker: Silvia Nagy

MITP talk - Silvia Nagy.pdf

11 The Newman-Penrose Map and the Classical Double Copy

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.

Speaker: Kara Farnsworth

DCWorkshop_Farnsworth.pdf

The Newman-Penrose Map and the Classical Double Copy (arXiv link)

12 Double-copy and unitarity of tree-level string amplitudes

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.

Speaker: Sebastian Mizera

Sebastian Mizera - YOUNGST@RS Rebuilding the Tower of Babel.pdf

13 Twistor amplitudes and CK duality

TBA

Speaker: Alfredo Guevara González

14 Geometry-kinematics duality and soft theorems

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.

Speaker: Julio Parra-Martínez

Wednesday 13 April

15 Double Copying Exceptional Field Theories

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

Speaker: David Berman

babel.pdf

Double Copying Exceptional Field Theories

16 A Topologically Massive Double Copy

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

Speaker: Nathan Moynihan

17 Massive Color-Kinematics Duality and Well-Defined Double Copies

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.

Speaker: Mariana Carrillo González

Mitp workshop.pdf

18 Worldsheet description of Kerr interactions

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.

Speaker: Alexander Ochirov

MITP2022final.pdf

19 Maximally Supersymmetric Massive Gravity and the Double-Copy

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.

Speaker: Callum Jones

20 Bootstrapping the KLT Formula

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.

Speaker: Shruti Paranjape

MITP Workshop 2022.pdf

21 The double copy and gravitational waves

Speaker: Zvi Bern

22 Closing