Ambitwistor strings and the scattering equations (1311.2564v1)

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.

• The paper introduces ambitwistor strings to simplify conventional string theory by focusing exclusively on massless modes and directly deriving the scattering equations.
• It employs a chiral, holomorphic worldsheet framework that naturally enforces null momentum constraints to ensure gauge invariance and unitarity.
• The approach bridges string theory with gauge and gravity amplitude computations using innovative Pfaffian structures and KLT relations.

Ambitwistor Strings and the Scattering Equations: An Overview

The paper "Ambitwistor strings and the scattering equations" by Lionel Mason and David Skinner introduces innovative formulations of string theories—termed ambitwistor strings—that simplify conventional string theory to focus solely on massless particles in critical dimensions. The ambitwistor string framework provides a structure that leads directly to the scattering equations identified by Cachazo, He, and Yuan for massless particles. This paper places these equations at the forefront and connects them fundamentally with underlying geometry.

Core Concepts and Theoretical Framework

Ambitwistor Space

A central concept is the notion of ambitwistor space, which extends ideas from traditional twistor theory. Ambitwistor space is the space of complex null geodesics or lightlike trajectories in a complexified spacetime. For bosonic string theory, ambitwistor space retains only massless solutions by focusing on null geodesics and completely decouples the massive modes, characteristic of high-tension string limits.

Symplectic and Chiral Structure

The ambitwistor string manifests its chiral structure by preserving only the holomorphic (complex analytic) aspects, leading to the formulation of worldsheet actions characterized by constraints such as $P^2=0$ corresponding to null momenta. These constraints naturally enforce scattering on specific solutions, the scattering equations, essential for particle dynamics.

RNS and Type II Ambitwistor Strings

Mason and Skinner explore both bosonic and supersymmetric ambitwistor string models. The RNS-like model, highlighting a chiral $N=2$ supersymmetry, produces ten-dimensional supergravity amplitudes without the massive string modes. Incompatibilities between zero-mode solutions and massive string excitations come from the consistency conditions imposed during quantization, leading to a purely massless string spectrum.

Scattering Amplitudes and Calculation

The ambitwistor models align precisely with the representation of scattering amplitudes found by Cachazo, He, and Yuan, showcasing permutation invariance and necessitating solutions to the scattering equations. The chiral framework simplifies calculations by intertwining worldsheet gauge theory with the conformal structure of scattering amplitudes, effectively capturing Yang-Mills and gravity amplitudes.

Examples and Calculations

An important outcome is the Pfaffian structure in the expressions for gravitational amplitudes and the inherent links to Yang-Mills theory via Kawai-Lewellen-Tye (KLT) relations. These mathematical objects ensure gauge invariance and correct physical properties (like unitarity) and demonstrate a clear computational advantage.

Implications and Further Research

Manifestations in Low- and Higher-Dimensional Theories

While the primary focus is in critical dimensions (10 for superstrings), the authors speculate on adapting the structures for diverse dimensions, potentially aiding in loop-level amplitude computations and investigating ultraviolet (UV) behaviors of space-time theories.

Potential and Expansion

The introduction of ambitwistor strings as foundational theoretical tools has implications for further exploration, such as scaling geometries and geometries of scattering. They encourage revisiting traditional concepts like modular invariance, potentially impacting the analysis of string theory in singular and complex environments.

Linking to Other Theories

The connection of ambitwistor geometry with existing gauge theory formulations opens doors to refining the comprehension of dualities and symmetry principles. Developing a full nonlinear framework might offer insights into quantum gravitational interactions.

Conclusion

By anchoring string theory directly to massless modes and underpinning the scattering equations, this innovative approach rewrites the narrative on classical field theory inputs into perturbative string theory. It enforces a resilient connection to both computational techniques and abstract formalism, paving the way for substantial advancements in understanding string theory’s applicability across various energy scales and dimensions.