S-duality and the double copy

Abstract

The double copy formalism provides an intriguing connection between gauge theories and gravity. It was first demonstrated in the perturbative context of scattering amplitudes but recently the formalism has been applied to exact classical solutions in gauge theories such as the monopole and instanton. In this paper we will investigate how duality symmetries in the gauge theory double copy to gravity and relate these to solution generating transformations and the action of SL(2, R) in general relativity.

Weyl doubling

“…In four dimensions, an analysis of the action of duality transformations [77,94] shows that this is the same σ as in equation (2.2). See also [95,96] where this was seen earlier using the spinor formalism in Type D spacetimes and more recently [97,98] for related work in higher dimensions.…”

“…In [60] four-dimensional type D spacetimes were investigated, using a double copy formula for the Weyl curvature spinor in terms of a Maxwell spinor. Duality symmetries of gauge theories and their relationship to solution-generating maps in gravity have also been studied recently from the point of view of the double copy [75,77]. The earlier work of [94] had used a self-dual Maxwell field, defined in terms of a Killing vector on the spacetime, in order to study how the Weyl tensor transformed under sl (2, R), and noted in particular that if the Weyl tensor was given by a suitable function quadratic in the Maxwell field, then the sl(2, R)-transformed metric also had a Weyl tensor satisfying this property.…”

“…The earlier work of [94] had used a self-dual Maxwell field, defined in terms of a Killing vector on the spacetime, in order to study how the Weyl tensor transformed under sl (2, R), and noted in particular that if the Weyl tensor was given by a suitable function quadratic in the Maxwell field, then the sl(2, R)-transformed metric also had a Weyl tensor satisfying this property. In [77] we, with Peinador Veiga, studied various metrics for which this is the case, showing how they transform under duality. This work, and that of [60], suggested that it would be interest to study cases where the Weyl tensor is given in terms of an Abelian gauge field, by what we will call "Weyl doubling".…”

Monopoles, shockwaves and the classical double copy

“…[47,[98][99][100] for further details. 5 Recently, the known electromagnetic duality relating electric and magnetic charges has been explored from a double copy point of view [83,107,108]. 6 A related programme of work has shown that a classical double copy is possible in arbitrary coordinate systems, if one restricts to linearised level only [52-56, 59, 60, 109].…”

The convolutional double copy: a case study with a point

“…Since its inception, a number of approaches have tried to extend its remit to classical solutions, exact or otherwise. Examples include the use of Kerr-Schild coordinates [4][5][6][7][8][9][10][11][12][13][14], spinorial methods [15,16], worldline methods [17][18][19][20][21], perturbative diagrammatic reasoning [22][23][24][25], and double field theory [26,27]. In this paper, we will focus on another approach, first introduced in ref.…”