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September 5, 2025Open Access

Vertex operators for the superstring with manifest d = 6 N = 1 supersymmetry

Key Points

Constructed a manifestly supersymmetric vertex operator U using d = 6 superspace variables and bosonic ghosts.
Demonstrated that BRST invariance of vertex operator U leads to SYM equations of motion in superspace.
Computed scattering amplitudes using methods similar to non-minimal pure spinor formalism with d = 6.
Provides new insights into the interaction of vertex operators and supersymmetry in superstring theory.

Abstract

A bstract By extending the six-dimensional hybrid formalism for the superstring to include d = 6 N N = 1 superspace variables along with unconstrained bosonic ghost fields, we construct a manifestly spacetime supersymmetric vertex operator U. We demonstrate that the BRST invariance of U implies the d = 6 N N = 1 SYM equations of motion in superspace. Furthermore, we show that spacetime supersymmetric scattering amplitudes can be computed in a manner analogous to that of the non-minimal pure spinor formalism.

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