Gravity and gauge theories

Colour-kinematics duality

Three of the four fundamental forces of nature are described by the Standard Model of particle physics. The only exception is the gravitational force. For gravity we do not have a rigorous quantum theory yet. In recent years hints and indications have emerged which support the assumption, that gravity is closely related to gauge theories. The origin of this idea can be traced back to the Kawai-Lewellen-Tye-relations between closed and open string amplitudes, however the idea can be stated without recourse to string theory. In particular, Bern, Carrasco and Johansson argue that gravity can be seen as a double copy of a gauge theory. The 'double copy'-property relies on the fact, that a scattering amplitude in a gauge theory can always be written in such a way, that the kinematical numerators satisfy a Jacobi-like relation whenever the associated group-theoretical factors do. This is a 'hidden' property of gauge theories, as 'standard' representations of scattering amplitudes do not have this property. This is a nice example where a hidden mathematical structure in quantum field theory gives us a hint on physics not included in the Standard Model.

Talks on this subject:

• Talk given at Loops and Legs, Leipzig, April 2016, arXiv:1606.07593 [hep-th].

Selected publications on this subject:

• Leonardo de la Cruz, Alexander Kniss, and Stefan Weinzierl, Double Copies of Fermions as Matter that Interacts Only Gravitationally, Phys. Rev. Lett. 116, 201601, arXiv:1601.04523 [hep-th].
• Leonardo de la Cruz, Alexander Kniss, and Stefan Weinzierl, The CHY representation of tree-level primitive QCD amplitudes, JHEP 1511 (2015) 217, arXiv:1508.06557 [hep-th].
• Leonardo de la Cruz, Alexander Kniss, and Stefan Weinzierl, Proof of the fundamental BCJ relations for QCD amplitudes, JHEP 1509 (2015) 197, arXiv:1508.01432 [hep-th].
• S. Weinzierl, On the solutions of the scattering equations, JHEP 1404, (2014), 092, arXiv:1402.2516 [hep-th].
• M. Tolotti and S. Weinzierl, Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality, JHEP 1307, (2013), 111, arXiv:1306.2975 [hep-th].