Topology and Wilson lines: global aspects of the double copy

Abstract

The Kerr-Schild double copy relates exact solutions of gauge and gravity theories. In all previous examples, the gravity solution is associated with an abelian-like gauge theory object, which linearises the Yang-Mills equations. This appears to be at odds with the double copy for scattering amplitudes, in which the non-abelian nature of the gauge theory plays a crucial role. Furthermore, it is not yet clear whether or not global properties of classical fields-such as non-trivial topology-can be matched between gauge and gravity theories. In this paper, we clarify these issues by explicitly demonstrating how magnetic monopoles associated with arbitrary gauge groups can be double copied to the same solution (the pure NUT metric) in gravity. We further describe how to match up topological information on both sides of the double copy correspondence, independently of the nature of the gauge group. This information is neatly expressed in terms of Wilson line operators, and we argue through specific examples that they provide a useful bridge between the classical double copy and the BCJ double copy for scattering amplitudes.

Post-Minkowskian effective field theory for conservative binary dynamics

“…Unfortunately, at the moment, we have not found a simple way to incorporate these tools into the EFT formalism, although ideas from the classical doubly copy, e.g. [111][112][113][114][115][116][117][118][119][120][121], may ultimately provide a hybrid framework to march smoothly towards higher orders.…”

“…some hybrid approach between the two (plausibly in combination with the classical double copy [111][112][113][114][115][116][117][118][119][120][121], on-shell methods [103,104], soft limits [90], and simplifications of the Einstein-Hilbert action [110]). In either case, the B2B dictionary [1,2] provides a direct (analytic) connection between scattering data and bound states, neatly demonstrating the need to push the computations to (even) higher orders, to fully incorporate the power of the PM expansion in the dynamics of binary systems.…”

The Newman-Penrose map and the classical double copy

“…On the gauge theory side, Wilson loops, or more generally, spin networks, are natural, gauge invariant quantities with clear gravitational analogues. Recently, progress along this direction was made by using gravitational Wilson line operators, defined in terms of the linearized graviton field, to match certain topological information on both sides of the double copy in a way that is gauge invariant [70]. It would be interesting to study such properties using the Newman-Penrose map where it may be natural to construct coordinate invariant gravitational Wilson lines (constructed out of the connection) and study their behavior under the map.…”

From Navier-Stokes to Maxwell via Einstein

“…As an example, the single copy of the Schwarzschild black hole metric is the field arrangement due to a color charge at the origin, when the dilaton expectation value is tuned to zero [36]. Many other examples of the classical double copy have been built [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53], including to some broad classes of spacetime [54]. Furthermore [55][56][57][58][59][60][61][62][63][64] have used this classical mapping to improve the perturbative series used in analytic calculations of black hole collisions.…”