Abstract
We show that double field theory arises from the color-kinematic double copy of Yang-Mills theory. A precise double copy prescription for the Yang-Mills action at quadratic and cubic order is provided that yields the double field theory action in which the duality invariant dilaton has been integrated out. More precisely, at quadratic order this yields the gauge invariant double field theory, while at cubic order it yields the cubic double field theory action subject to a gauge condition that originates from Siegel gauge in string field theory.
Highlights
The fundamental interactions in nature, as far as currently known, are governed by two kinds of theories: YangMills theory, which describes the gauge bosons of the standard model of particle physics, and Einstein’s theory of general relativity, which describes the force of gravity and the universe at large
Theories on toroidal backgrounds [15]. While this theory has not yet been constructed explicitly beyond cubic order, much work has been done on strongly constrained double field theory, in which the doubling of coordinates is purely formal but which provides a duality covariant and background-independent reformulation of the target space actions of string theory including metric, B field, and dilaton. (See [19] for reviews and [20] for earlier important work.) It was anticipated by Siegel in [14] that these reformulations render index factorizations manifest, and this was established explicitly to all orders in fields in [21] and used in [22] for amplitude computations. (See [23], where the problem of index factorizations was revisited more recently, and [24,25,26] for double copy prescriptions of classical solutions in double field theory.)
The key technical result reported here is that this double copy of Yang-Mills theory yields at quadratic and cubic order double field theory upon integrating out the duality invariant dilaton
Summary
The fundamental interactions in nature, as far as currently known, are governed by two kinds of theories: YangMills theory, which describes the gauge bosons of the standard model of particle physics, and Einstein’s theory of general relativity, which describes the force of gravity and the universe at large. Factors by kinematic factors yields gravity amplitudes, whose computation by standard textbook methods starting from the Einstein-Hilbert Lagrangian is incomparably more involved; see [3] for a recent review and [4] for a popular account Somewhat misleadingly, these observations are often summarized by “gravity is Yang-Mills squared.”. DÍAZ-JARAMILLO, HOHM, and PLEFKA theories on toroidal backgrounds [15] While this theory has not yet been constructed explicitly beyond cubic order, much work has been done on strongly constrained double field theory, in which the doubling of coordinates is purely formal but which provides a duality covariant and background-independent reformulation of the target space actions of string theory including metric, B field, and dilaton. The key technical result reported here is that this double copy of Yang-Mills theory yields at quadratic and cubic order double field theory upon integrating out the duality invariant dilaton. More precisely, at quadratic order this match holds at the level of gauge-invariant Lagrangians, while at cubic order this match requires a gauge choice, which in the string field theory formulation of [15] originates from the so-called Siegel gauge and which reduces to the de Donder gauge for standard gravity fields
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