Manifest Moebius invariance of massive tree-level three-point amplitudes in pure spinor superspace

TL;DR

The paper presents a new Moebius-invariant representation of massive three-point open-string amplitudes in pure spinor superspace, confirmed by explicit calculations and extended through BRST recurrence relations.

Contribution

It introduces a compact nested-bracket form of the amplitudes with manifest Moebius invariance and extends the results to arbitrary mass levels using BRST recursions.

Findings

Explicit superspace calculations confirm Moebius invariance.

New BRST recurrence relations are derived for arbitrary mass levels.

A manifestly Moebius-invariant expression for massive three-point amplitudes is provided.

Abstract

Using BRST cohomology properties in pure spinor superspace and identities for OPE brackets of non-free fields, we obtain a new compact nested-bracket representation of massive tree-level three-point open-string amplitudes in which Moebius invariance is manifest. Explicit superspace calculations for amplitudes with level-one massive states confirm this finding, and we derive new BRST recurrence relations among three-point numerators to extend the result to arbitrary mass levels. This provides a manifestly Moebius-invariant expression for massive three-point amplitudes in the pure spinor formalism.