NS-NS Spacetimes from Amplitudes

Abstract

Recent work has shown how on-shell three-point amplitudes in gauge theory and gravity, representing the coupling to massive particles, correspond in the classical limit to the curvature spinors of linearised solutions. This connection, made explicit via the KMOC formalism in split metric signature, turns the double copy of scattering amplitudes into the double copy of classical solutions. Here, we extend this framework to the universal massless sector of supergravity, which is the complete double copy of pure gauge theory. Our extension relies on a Riemann-Cartan curvature incorporating the dilaton and the B-field. In this setting, we can determine the most general double copy arising from the product of distinct gauge theory solutions, say a dyon and √ Kerr. This gives a double-copy interpretation to gravity solutions of the type Kerr-Taub-NUT-dilaton-axion. We also discuss the extension to heterotic gravity. Finally, we describe how this formalism for the classical double copy relates to others in the literature, namely (i) why it is an on-shell momentum space analogue of the convolutional prescription, and (ii) why a straightforward prescription in position space is possible for certain vacuum solutions.

The SAGEX Review on Scattering Amplitudes, Chapter 14: Classical Gravity from Scattering Amplitudes

“…Notice that it is highly non-trivial that the same solutions can satisfy equation ( 110) and, at linearised level, equation (109), which is the statement most directly connected to the double copy of three-point amplitudes. This fact relies on the details of the solutions, as worked out recently for Kerr-Taub-NUT spacetimes [132]. We will return to this point.…”

“…Considering both deformations together [128], it is easy to see that the linearisation of the Kerr-Taub-NUT solution is a double copy of a spinning dyon solution, obtained via a Newman-Janis shift of the dyon. It is further possible to consider double copies involving the product of amplitudes for opposite helicities, thereby making contact with solutions involving non-trivial dilatons and axions [132], as we will discuss in the next section.…”

“…Similar (2, 2) signature constructions of linearised solutions from scattering amplitudes to that presented in refs. [125,132] were discussed in refs. [124,134].…”

“…In order to extend this beyond vacuum gravity, ref. [132] introduced a generalised curvature, based on Riemann-Cartan geometry, which incorporates the graviton, the dilaton and the B-field. This is precisely the curvature of the fat graviton field H µν of [179].…”

The Gauge Structure of Double Field Theory follows from Yang-Mills Theory

“…In the homotopy algebra formulation these solutions are given by the Maurer-Cartan elements corresponding to the L ∞ structure. It would be interesting to investigate this in detail and to compare with existing attempts in the literature on establishing double copy relations at the level of classical solutions [44][45][46].…”