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

On the kinematic algebra for BCJ numerators beyond the MHV sector
20190626arXiv:1906.10683
UUITP22/19
NORDITA 2019064
HUEP19/17
QMULPH1914
by: Chen, Gang
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 amplitudes: up to the MHV sector. In this paper we introduce a fram... 
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... 
Unraveling conformal gravity amplitudes
20180614arXiv:1806.05124
UUITP24/18
NORDITA 2018042
UUITP2418
NORDITA2018042
JHEP 1809 (2018) 080
by: Johansson, Henrik (Uppsala U.) et al.
Abstract:
Conformal supergravity amplitudes are obtained from the doublecopy construction using gaugetheory amplitudes, and compared to direct calculations starting from conformal supergravity Lagrangians. We consider several different theories: minimal $ \mathcal{N}=4 $ conformal supergravity, nonminimal $ \mathcal{N}=4 $ BerkovitsWitten conformal supergravity, massdeformed versions ... 
Ultraviolet Properties of $\mathcal N = 8$ Supergravity at Five Loops
20180426arXiv:1804.09311
Phys.Rev. D98 (2018) 086021
by: Bern, Zvi (UCLA) et al.
Abstract:
We use the recently developed generalized doublecopy construction to obtain an improved representation of the fiveloop fourpoint integrand of N=8 supergravity whose leading ultraviolet behavior we analyze using stateoftheart loopintegral expansion and reduction methods. We find that the fiveloop critical dimension where ultraviolet divergences first occur is Dc=24/5, corresponding to a D8R4 counterterm. This ultraviolet behavior stands in contrast to the ...