On the soft limit of open string disk amplitudes with massive states

TL;DR

This paper investigates the universal behavior of open string disk amplitudes involving gluons and massive states in the soft limit, demonstrating universality similar to Yang-Mills theories through explicit calculations and formal analysis.

Contribution

It shows that the leading and sub-leading soft terms are universal for open string amplitudes with massive states, extending the understanding of soft behavior beyond massless cases.

Findings

Soft terms are universal and match Yang-Mills results.

Explicit 4-point amplitude calculations support the universality.

Validation of a formula relating superstring and SYM amplitudes.

Abstract

We discuss the soft behaviour of open string amplitudes with gluons and massive states in any dimension. Notwithstanding non-minimal couplings of massive higher spin states to gluons, relying on OPE and factorization, we argue that the leading and sub-leading terms are universal and identical to the ones in Yang-Mills theories. In order to illustrate this, we compute some 4-point amplitudes on the disk involving gluons, massive states and, for the bosonic string, tachyons. For the superstring, we revisit the structure of the massive super-multiplets at the first massive level and rewrite the amplitudes in D = 4 in the spinor helicity formalism, that we adapt to accommodate massive higher spin states. We also check the validity of a recently obtained formula relating open superstring amplitudes for mass-less states at tree-level to SYM amplitudes, by factorisation on two-particle massive poles. Finally we analyse the holomorphic soft limit of superstring amplitudes with one massive insertion.