All Tree Amplitudes of 6D $(2,0)$ Supergravity: Interacting Tensor Multiplets and the $K3$ Moduli Space

Abstract

We present a twistor-like formula for the complete tree-level S matrix of 6D $(2,0)$ supergravity coupled to $21$ abelian tensor multiplets. This is the low-energy effective theory that corresponds to Type IIB superstring theory compactified on a $\mathrm{K}3$ surface. The formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, $\frac{SO(5,21)}{SO(5)\times SO(21)}$. Finally, by dimensional reduction, we also obtain a new formula for the tree-level S matrix of 4D $\mathcal{N}=4$ Einstein-Maxwell theory.

arXiv comment6 pages + references, minor revisions

References in corpus (18)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Scattering of Massless Particles in Arbitrary Dimension
• What is the Simplest Quantum Field Theory?
• Some Comments On String Dynamics
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• On the Tree-Level S-Matrix of Yang-Mills Theory
• K3 Surfaces and String Duality
• Amplitudes and Spinor-Helicity in Six Dimensions
• Scattering in Three Dimensions from Rational Maps
• On-shell superamplitudes in N<4 SYM
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• The polarized scattering equations for 6d superamplitudes
• M5-Brane and D-Brane Scattering Amplitudes
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• Consistency conditions from generalized-unitarity
• A String Deformation of the Parke-Taylor Factor
• Supersymmetry Constraints and String Theory on K3
• Anomalies without an action

Cited by in corpus (18)

• Aspects of Scattering Amplitudes and Moduli Space Localization
• The Momentum Amplituhedron
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
• Holographic correlators in AdS${}_3$ without Witten diagrams
• Maximal $U(1{)}_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• The orthogonal momentum amplituhedron and ABJM amplitudes
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• Spinor-helicity formalism for massive and massless amplitudes in five dimensions
• On Chiral Splitting and the Ambitwistor String
• Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian
• Supersymmetric S-matrices from the worldsheet in 10 and 11d
• Notes on gravity multiplet correlators in $Ad{S}_3\times S^3$
• Recursion and worldsheet formulae for 6d superamplitudes
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• M5-Brane Amplitudes
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D