Abstract
We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space-time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree-level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories.
Highlights
Of spins 0, 1 or 2 in arbitrary dimension
We have presented worldsheet models whose n-point correlation functions at genus zero reproduce the new representations of tree-level gravitational, Yang-Mills and scalar amplitudes presented in [9]. These representations are supported on solutions of the scattering equations (1.2) by virtue of the origin of the wave functions as cohomology classes on ambitwistor space
The amplitudes for particles of different spin came from different string theories, with the scalar, Yang-Mills and gravitational amplitudes arising from the bosonic, ‘heterotic’ and ‘type II’ ambitwistor strings, respectively
Summary
The target space of the string theories we construct will be the space of complex null geodesics in complexified space-time M. To obtain the space A of scaled complex null geodesics, we must quotient TN∗ M by the action of This vector is the horizontal lift of the space-time derivative pμ∂μ to the cotangent bundle T ∗M using the Levi-Civita connection Γ associated to g. The main differences are that i) the ambitwistor wavefunction is non-chiral and is defined in arbitrary dimensions, and ii) neither the momentum nor the (symmetric, trace-free) polarization vector are constrained in the ambitwistor wavefunction At this stage we do note require k2 = 0 or kμ μν = 0. This is in keeping with the fact that holomorphic objects on ambitwistor space are not manifestly on-shell objects in space-time As mentioned above, these constraints will arise from quantum consistency of the string theory, but it is worth noting that the formulae of [9, 10] involve polarization vectors μν and momenta k — their representation of amplitudes is not manifestly on-shell. We remark that in the context of the ambitwistor string path integral, the factor of δ(k · p) in the ambitwistor wavefunction for a momentum eigenstate provides the origin of the constraint to solutions of the scattering equations in the formulae of [9, 10]
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