Henrik Johansson

Henrik Johansson phone: +46(0)18 471 3243 
RESEARCH
My research interests are in quantum field theory and supergravity, with a focus on formal aspects of scattering amplitudes in these theories. Scattering amplitudes can be used as a powerful tool to understand hidden symmetries and remarkable relations between different classes of theories. My work has led to the realization that a generic gravity theory can be formally understood as a product of two gauge theories.
KAW project – From Scattering Amplitudes to Gravitational Waves
This project will develop new methods for precise calculations at the forefront of theoretical
physics, ranging from scattering processes in quantum field theory to gravitational wave
emission, by using the BernCarrascoJohansson (BCJ) doublecopy framework, that
connects gauge, gravity and string theories. The project will involve cooperation between
the Division of Theoretical Physics at Uppsala University, and the Nordic Institute for Theoretical Physics (Nordita) that is located in Stockholm.
The project consists of five semiindependent parts:
 Develop new methods for gauge, gravity and string theory scattering amplitudes
 Simplify perturbative GR: potentials, blackhole mergers and gravitational waves
 Advance integration techniques for loop amplitudes and classical gravity
 Understand the origins of colorkinematics duality and the double copy
 Extend the double copy to curved spaces
Background: In one of my papers from 2008, we introduce the notion of a duality between kinematical quantities (spacetime quantities) and color quantities (internal space quantities). In this framework gauge theories are organized as a specific product of two copies of Lie algebras, one for the color degrees of freedom and one for the kinematical degrees of freedom. Gravitational theories are analogously organized as a double copy of the kinematical Lie algebras. This is most transparent for Smatrix elements, where this powerful structure has been used for amplitude calculations up to the fifth loop order in certain supersymmetric gauge and gravity theories.
There is by now a growing list of theories where the duality and doublecopy structures have been observed; it includes: pure (super)YangMills theories, pure (super)gravities, QCD and its supersymmetric extensions, YangMillsEinstein (super)gravities, the nonlinear sigma model (NLSM), BornInfeld theories and also string theory. Gauge and gravity theories are now more closely linked to each other than ever before, but even effective theories that have no gauge symmetry fit into the new picture. New connections to string theory have also emerged out of this structure: heterotic/closed string theories obeys colorkinematics duality and open string theories are double copies of simpler objects.
When the LIGO experiment in September 2015 discovered the first gravitational waves from binary black holes—which awarded them the 2017 Nobel Prize in Physics—a new window for observations of the universe opened up. In order to fully utilize this new opportunity, both theoretical calculation methods and experiments are expected to undergo significant upgrades in the future. Recent initial studies have convincingly demonstrated that the BCJ doublecopy method is able to reproduce loworder binary blackhole dynamics and associated gravitationalwave emissions at significantly reduced computational cost compared to standard methods, and as such it has the potential to revolutionize analytical calculations of gravitational waves.
TEACHING
Recent Publications

The Duality Between Color and Kinematics and its Applications
20190905arXiv:1909.01358
CERNTH2019135
UCLA/TEP/2019/104
NUHEPTH/1911
UUITP35/19, NORDITA 2019079
by: Bern, Zvi (UCLA) et al.
Abstract:
This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to looplevel calculations, the broad web of theories linked by the duality and the associated doublecopy structure, and the issue of extending the duality and do... 
Double copy for massive quantum particles with spin
20190701arXiv:1906.12292
UUITP24/19
NORDITA 2019070
JHEP 1909 (2019) 040
by: Johansson, Henrik (Uppsala U.) et al.
Abstract:
The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gaugegroup representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. In this paper we elaborate on the d... 
On the kinematic algebra for BCJ numerators beyond the MHV sector
20190626arXiv:1906.10683
UUITP22/19
NORDITA 2019064
HUEP19/17
QMULPH1914
JHEP 1911 (2019) 055
by: Chen, Gang (Zhejiang Normal U.) et al.
Abstract:
The duality between color and kinematics present in scattering amplitudes of YangMills theory strongly suggest the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of fourdimensional amplitu... 
The FullColor TwoLoop FourGluon Amplitude in $\mathcal{N} = 2$ SuperQCD
20190411arXiv:1904.05299
CERNTH2019042
CP31915
UUITP14/19
NORDITA 2019034
by: Duhr, Claude (CERN) et al.
Abstract:
We present the fully integrated form of the twoloop fourgluon amplitude in $\mathcal{N} = 2$ supersymmetric quantum chromodynamics with gauge group SU$(N_c)$ and with $N_f$ massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on $N_c$ and $N_f$, and relies on the existence of a compact integrand representation that exhibits the duality between color... 
NonAbelian gauged supergravities as double copies
20181227arXiv:1812.10434
UUITP62/18
NORDITA 2018130
JHEP 1906 (2019) 099
by: Chiodaroli, Marco (Uppsala U.) et al.
Abstract:
Scattering amplitudes have the potential to provide new insights to the study of supergravity theories with gauged Rsymmetry and Minkowski vacua. Such gaugings break supersymmetry spontaneously, either partly or completely. In this paper, we develop a framework for doublecopy constructions of Abelian and nonAbelian gaugings of N=8 supergravity with these properties. They are generally obtained as the double copy of...