Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms

Abstract

We present a geometric derivation of all-multiplicity (single-trace) tree-level Einstein Yang-Mills (EYM) amplitudes $\mathcal{A}(n;r)$ involving $n$ gluons and $r$ gravitons by a bilinear of two twisted differential forms on the moduli space of Riemann spheres with $m:=n+r$ punctures. The differential forms are gained by studying the underlying superstring disk amplitude and proposing an embedding of the disk onto the sphere. This map can be interpreted as a geometrical map from the open superstring to a heterotic or ambitwistor string structure. Then, the twisted intersection number of the two $m$-forms, which is obtained by integrating over the moduli space of Riemann sphere with $m$ punctures, reproduces in the infinite inverse string tension limit ${\alpha }^{\prime }\to \infty$ the corresponding CHY formula of the EYM amplitude. To bolster our findings we study the disk amplitude of open and closed strings using the Grassmann description of the underlying superstring amplitude, map it to a closed string amplitude and consider the ${\alpha }^{\prime }\to \infty$ limit. Finally, we present an all-multiplicity decomposition formula of any EYM amplitude $\mathcal{A}(n;r)$ as linear combination over $(m-3)!$ pure $m$ gluon subamplitudes.

arXiv comment40 pages, LaTeX; v2: improved version, typos removed and subsection 6.3 added

References in corpus (33)

• New Relations for Gauge-Theory Amplitudes
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Minimal Basis for Gauge Theory Amplitudes
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Ambitwistor strings and the scattering equations
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Motivic Multiple Zeta Values and Superstring Amplitudes
• Scattering Amplitudes from Intersection Theory
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• On the Coupling of Gravitons to Matter
• Aspects of Scattering Amplitudes and Moduli Space Localization
• On the null origin of the ambitwistor string
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• New Relations for Einstein-Yang-Mills Amplitudes
• Expansion of Einstein-Yang-Mills Amplitude
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Monodromy Relations in Higher-Loop String Amplitudes
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Higher-loop amplitude monodromy relations in string and gauge theory
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Expansion of All Multitrace Tree Level EYM Amplitudes
• SD Perturbiner in YM+Gravity
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• Subleading Terms in the Collinear Limit of Yang-Mills Amplitudes
• Disk Scattering of Open and Closed Strings (I)
• Monodromy relations from twisted homology
• Graviton as a Pair of Collinear Gauge Bosons
• Graviton Amplitudes from Collinear Limits of Gauge Amplitudes
• Gravitationally dressed Parke-Taylor amplitudes
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d

Cited by in corpus (2)

• Tree-level amplitudes from the pure spinor superstring
• One-loop amplitudes in Einstein-Yang-Mills from forward limits