F-theory amplitudes

Abstract

We propose 4-point S-matrices for three-dimensional F-theory. We will use the twistor formalism to facilitate constructing the amplitude. We write the amplitude in a way such that the F-symmetry (U-duality symmetry) is manifest. The amplitude can be schematically written as $A_4=w^4/stu$, where $w$ is an analog of the linearized Weyl tensor in F-theory, and $w^4$ is a shorthand for the sum of various contractions that can happen between the Weyl tensors. The gauge invariance is actually non-trivial since $w$ is in general not gauge invariant. With the help of the twistor formalism, one can verify that this formula is indeed gauge invariant. The amplitude also reduces to the ordinary 4-graviton amplitude under the reduction to M-theory (which is just 4D supergravity).

26 pages. This paper is compiled in LuaTex. The source can be found at http://insti.physics.sunysb.edu/~siegel/tex.shtml

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• Gluon scattering amplitudes at strong coupling
• T-duality off shell in 3D Type II superspace
• Exceptional geometry and tensor fields
• F-theory superspace backgrounds
• F-brane Superspace: The New World Volume