The pure spinor superparticle and 10D super-Yang-Mills amplitudes

TL;DR

This paper develops a covariant, BRST-invariant method using pure spinor worldline formalism to compute tree-level scattering amplitudes in 10D super-Yang-Mills theory, aligning with superstring results.

Contribution

It introduces a novel first-quantized pure spinor worldline approach for 10D SYM amplitudes, bridging field theory and string theory frameworks.

Findings

Explicit N-point amplitude computations match superstring limits.

Kinematic numerators satisfy BRST invariance.

Method paves the way for applications to 11D supergravity.

Abstract

We present a prescription for computing tree-level scattering amplitudes in 10D super-Yang-Mills (SYM) theory using the pure spinor worldline formalism. The pure spinor formalism has proven to be a powerful framework for studying supersymmetric field theories, providing manifestly covariant and BRST-invariant formulations of amplitudes. By incorporating the worldline approach, we construct a first-quantized representation of SYM amplitudes in 10D, where interactions are encoded through the insertion of vertex operators along the particle's trajectory. We explicitly compute the N-point function, demonstrating an agreement with the limit $\alpha' \to 0$ of open superstring amplitudes and confirming that the kinematic numerators satisfy the expected BRST relations. Our results establish the pure spinor worldline formalism as a tool for studying scattering amplitudes and suggest further applications to 11D supergravity.