Scattering of Massless Particles in Arbitrary Dimension

Abstract

We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. The new formula for the scattering of n particles is given by an integral over the position of n points on a sphere restricted to satisfy a dimension-independent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n by 2n matrix that depends on momenta and polarization vectors. In its simplest form, the gravity integrand is a reduced determinant which is the square of the Pfaffian in the Yang-Mills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.

v2: Simpler form for gravity added. Argument below eq. 14 streamlined. 4 pages, 2 columns

References in corpus (6)

• New Relations for Gauge-Theory Amplitudes
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Minimal Basis for Gauge Theory Amplitudes
• Ambitwistor strings and the scattering equations
• Infinite Tension Limit of the Pure Spinor Superstring
• Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension

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