Monopoles, shockwaves and the classical double copy

Abstract

The classical double copy relates exact solutions in biadjoint scalar, gauge and gravity theories. Recently, nonperturbative solutions have been found in biadjoint theory, which have been speculated to be related to the Wu-Yang monopole in gauge theory. We show that this seems not to be the case, by considering monopole solutions in the infinitely boosted (shockwave) limit. Furthermore, we show that the Wu-Yang monopole is instead related to the Taub-NUT solution, whose previously noted single copy is that of an abelian-like (Dirac) monopole. Our results demonstrate how abelian and non-abelian gauge theory objects can be associated with the same gravity object, and clarify a number of open questions concerning the scope of the classical double copy. 1 n.bahjat-abbas@qmul.ac.uk

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.…”

Topology and Wilson lines: global aspects of the double copy

“…Thus, we provide an explicit example of an exact solution whose local and global properties obey the construction of figure 1, and which fully generalises the preliminary observations regarding SU(2) monopoles made recently in ref. [85]. Furthermore, we will see that all of our patching conditions -in either gauge or gravity theories -can be expressed in terms of certain Wilson line operators.…”

“…Indeed, figure 1 has a precedent in the study of infrared singularities of amplitudes [27], and was also considered for solutions of SU(2) gauge theory in ref. [85] (see refs. [35,36] for yet more examples).…”

“…One way to probe this is to find explicit non-perturbative solutions in theories that enter the double copy correspondence, such as the biadjoint scalar theory considered in refs. [82][83][84][85]. There is, however, another approach to extending the conceptual framework of the double copy.…”

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.…”