Abstract
We present all-multiplicity formulas for the tree-level scattering of gluons and gravitons in the maximal helicity violating (MHV) helicity configuration, calculated in certain chiral strong fields. The strong backgrounds we consider are self-dual plane waves in gauge theory and general relativity, which are treated exactly and admit a well-defined S matrix. The gauge theory background-coupled MHV amplitude is simply a dressed analog of the familiar Parke-Taylor formula, but the gravitational version has nontrivial new structures due to graviton tails. Both formulas have just one residual integral rather than the n-2 expected at n points from space-time perturbation theory; this simplification arises from the integrability of self-dual backgrounds and their corresponding twistor description. The resulting formulas pass several consistency checks and limit to the well-known expressions for MHV scattering of gluons and gravitons when the background becomes trivial.
Highlights
Introduction.—One hallmark of recent advances in the study of perturbative quantum field theories (QFTs) is the ability to find all-multiplicity expressions for scattering amplitudes
We present all-multiplicity formulas for the tree-level scattering of gluons and gravitons in the maximal helicity violating (MHV) helicity configuration, calculated in certain chiral strong fields
There are all-multiplicity formulas for the full tree-level S matrices of gauge theory, gravity, and many other massless QFTs in diverse spacetime dimensions, and a growing list of allmultiplicity formulas in some theories beyond tree level. These formulas are in the “standard” setting of perturbative QFT—where the perturbative expansion occurs around a trivial field configuration—but there are myriad settings of physical interest where scattering in the presence of nontrivial, or strong, background fields must be considered
Summary
Are structurally reminiscent of all-multiplicity formulas in a trivial background, but with significant novel features. MHV amplitudes.—It is straightforward to prove that all tree-level amplitudes in SDPWs with one or zero negative helicity gluons or gravitons vanish; this is a consequence of the integrability of the self-dual sector in gauge theory and gravity [40]. The exponential phase appearing in the residual light-front integration is a n-point generalization of an object appearing at lower points in strong field QED, known as the Volkov exponent [35,42] This is defined by a composite momentum K built from any set of n − 1 distinct dressed gluon momenta; for instance,
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