Abstract
The scattering equation formalism for scattering amplitudes, and its stringy incarnation, the ambitwistor string, remains a mysterious construction. In this paper, we pursue the study a gauged-unfixed version of the ambitwistor string known as the null string. We explore the following three aspects in detail; its complexification, gauge fixing, and amplitudes. We first study the complexification of the string; the associated symmetries and moduli, and connection to the ambitwistor string. We then look in more details at the leftover symmetry algebra of the string, called Galilean conformal algebra; we study its local and global action and gauge-fixing. We finish by presenting an operator formalism, that we use to compute tree-level scattering amplitudes based on the scattering equations and a one-loop partition function. These results hopefully will open the way to understand conceptual questions related to the loop expansion in these twistor-like string models.
Highlights
The extension of some recent developments at one and higher loops [17,18,19] may rely on a deeper understanding of these questions
We look in more details at the leftover symmetry algebra of the string, called Galilean conformal algebra; we study its local and global action and gauge-fixing
We finish by presenting an operator formalism, that we use to compute tree-level scattering amplitudes based on the scattering equations and a one-loop partition function
Summary
The null string was originally obtained by Schild as a tensionless limit of the Nambu-Goto string [21]. At this point the worldsheet itself is still a two dimensional real manifold This procedure gives a complexified version of the LST action where X : Σ → MCD and V ∈ Ω2(Σ) 2 ⊗ TCΣ are respectively, a map from the worldsheet to complexified Minkowski space MCD ≃ CD, and a complex vector field on the worldsheet with weight one half. Is enough to see that this is exactly the second order version of the ambitwistor action described in [4]: S[∂ ̄, e, X, P ] = Note that in this action, the complex structure is a field of the model, being integrated over, while the ambitwistor string is already gauge-fixed to conformal gauge. Integral lines of (V X)μ in space-time are null lines and these null lines are orthogonal to each other
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