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

TL;DR

The paper shows that open string disk amplitudes involving massive external states exhibit universal soft behavior at tree level, with leading and subleading terms identical to Yang-Mills theory. It bases this on world-sheet OPE and factorization arguments, and confirms the universality through explicit four-point calculations in both bosonic and superstring frameworks, including spinor-helicity formulations in D=4. It also validates the open-string–YM connection via the MSS formula for massless states and explores higher-point amplitudes, both in massless and massive channels. The results suggest a robust universality for the soft limit in open strings and point to interesting extensions to loops and closed-string (gravitational) cases, where subtleties like dilaton couplings may alter the leading behavior.

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.