The massive one-loop four-point string amplitude in pure spinor superspace

TL;DR

This paper computes one-loop four-point string amplitudes involving massless and massive states in pure spinor superspace, revealing relations to tree-level kinematic factors and differences between open and closed strings.

Contribution

It demonstrates that one-loop correlators for open strings can be expressed in terms of tree-level kinematic factors, and extends this to certain closed-string cases, highlighting new structural insights.

Findings

Open-string one-loop correlators relate to tree-level kinematic factors.

Closed-string four-point correlators can be rewritten similarly for specific state combinations.

Differences are identified between type IIA and IIB string theories in these relations.

Abstract

The open- and closed-string three- and four-point one-loop amplitudes involving massless states and one first-level massive state are computed in pure spinor superspace. For the open string, we show that their one-loop correlators can be rewritten in terms of tree-level kinematic factors. We then analyze the closed string. For three points, this is immediate. For four points, we show that it is possible to rewrite the one-loop closed-string correlator using tree-level kinematic factors, but only for certain combinations of massive and massless states (different for type IIA and IIB).