Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

Authors: Marco Chiodaroli, Murat Gunaydin, Henrik Johansson and Radu Roiban Preprint number: UUITP–41/23 Scattering amplitudes in Yang-Mills-Einstein theories has mainly been explored for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional ${\cal N}=2$ supergravities with non-compact gauge symmetries. On one side of the double copy is a SYM theory with a massive hypermultiplet and on the other is a particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. We also consider supergravities with massive self-dual tensors in five dimensions, showing that tensors are straightforwardly realized as double copies of gauge theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg algebras in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector-vector matter couplings.