The tree formula for MHV graviton amplitudes

Abstract

We present and prove a formula for the MHV scattering amplitude of n gravitons at tree level.Some of the more interesting features of the formula, which set it apart as being significantly different from many more familiar formulas, include the absence of any vestigial reference to a cyclic ordering of the gravitons-making it in a sense a truly gravitational formula, rather than a recycled Yang-Mills result, and the fact that it simultaneously manifests both S n−2 symmetry as well as large-z behavior that is O(1/z 2 ) term-by-term, without relying on delicate cancellations.The formula is seemingly related to others by an enormous simplification provided by O(n n ) iterated Schouten identities, but our proof relies on a complex analysis argument rather than such a brute force manipulation. We find that the formula has a very simple link representation in twistor space, where cancellations that are non-obvious in physical space become manifest.

Constructing amplitudes from their soft limits

“…We will use this result to uniquely define the form of the soft factor that we will use in studying gravity amplitudes. It should be noted that the soft factor we find is distinct from that presented in [21,25]. Since MHV amplitudes only contain two-particle factorization terms in BCFW, we will present a compact inverse-soft recursion relation for these amplitudes in gauge theory and gravity.…”

“…In [21], inverse soft was shown to reproduce MHV gravity amplitudes in the form first given in [22]. Very recently, inspired in part by the inverse-soft procedure discussed in [21], Hodges presented new expressions for MHV amplitudes [23].…”

“…Very recently, inspired in part by the inverse-soft procedure discussed in [21], Hodges presented new expressions for MHV amplitudes [23]. However, other than this result, the application of inverse soft to gravity amplitudes has been minimal.…”

“…The gravity soft factor in [21] cannot easily reproduce multiparticle factorization channels necessary to construct NMHV amplitudes. We find that its most natural generalization that can do so is a soft factor inspired by BCFW.…”

“…In any case, the BCFW recursion relations imply the inverse-soft recursion relation for MHV gravity amplitudes: 10) where the primes on the right side indicate the inverse-soft momentum deformation. Nguyen, et al, introduced in [21] a distinct inverse-soft construction of gravity MHV amplitudes. In constructing MHV amplitudes, they used…”