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 $$ \mathcal{G} $$ 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 $$ \mathcal{G} $$ 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.

Algebraic branch points at all loop orders from positive kinematics and wall crossing

“…Significant strides have been made in both understanding the underlying structure of amplitudes and developing new computation methods. Many techniques for computing amplitudes are under active research, such as the double copy [2][3][4], positive geometry [5][6][7], intersection theory [8][9][10] and much more [11][12][13][14][15][16][17][18]. In particular, a number of techniques have emerged that leverage non-perturbative properties of the S-matrix, such as unitarity and cluster decomposition.…”

“…We work with the degenerate cluster polytope instead of the degenerate scattering diagram. 18 Note that if one only tropicalizes a finite subset of O(X ∨ ), one often finds that the associated degenerate cluster polytope includes a facet corresponding to a limiting ray. 19 For example, consider the following principle quiver:…”

Non-planar BCFW Grassmannian Geometries

“…Understanding how to do without planar variables and cyclic symmetry is crucial for addressing open questions in perturbative gravity where the graviton amplitudes are intrinsically non-planar. And indeed there are many intriguing properties of graviton amplitudes such as color-kinematics duality [95][96][97], surprisingly compact formulas for tree-level amplitudes [98][99][100][101][102][103][104][105] or enhanced UV behavior of loop amplitudes [106][107][108][109][110], all of which suggest new formulations for amplitudes that extend beyond the planar sector.…”

Multi-spin soft bootstrap and scalar-vector Galileon

“…In the last few decades, we have seen many discoveries of hidden mathematical JHEP07(2021)153 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]. Surprisingly, some of these recent developments have also been found in the context of tree-level amplitudes in effective field theories.…”