Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes

Abstract

In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity analogues which we call G-invariants, and expand the NMHV gravity amplitudes in terms of these objects. We provide explicit formulas of NMHV gravity amplitudes up to eight points in terms of G-invariants, and give the general definition for any number of points. We discuss the connection to BCFW representation, special behavior under large momentum shift, the role of momentum twistors and the intricate web of spurious poles cancelation. Because of the close connection between R-invariants and the (tree-level) Amplituhedron for Yang-Mills amplitudes, we speculate that the new expansion for gravity amplitudes should correspond to the triangulation of the putative Gravituhedron geometry.

Multi-spin soft bootstrap and scalar-vector Galileon

“…In the last few decades, we have seen many discoveries of hidden mathematical structures and symmetries in the perturbative S-matrix which are completely invisible in the standard Feynman diagrams approach. Unitarity methods [1,2] and recursion relations exploit the locality and unitarity of tree-level amplitudes [3][4][5][6][7] and loop integrands [8,9], CHY formula evaluates tree-level amplitudes as worldsheet integrals [10,11], colorkinematics duality relates amplitudes in different theories simplifying significantly complex calculations [12][13][14], and in certain theories the S-matrix has been formulated in geometric language using positive geometries leading to Amplituhedron picture for planar N = 4 SYM amplitudes [15][16][17][18][19][20][21][22], and beyond [23][24][25][26][27].…”