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 subleading 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.
Highlights
Introduction and motivationsRecently the soft behaviour of scattering amplitudes has received renewed attention in connection with the extended BvBMS symmetry [1,2,3,4,5,6]
We discuss the soft behaviour of open string amplitudes with gluons and massive states in any dimension
It has been long known that gauge theory and gravity amplitudes expose universal behaviours when one of the mass-less external momenta is ‘soft’ i.e. k → 0 [7,8,9]
Summary
The soft behaviour of scattering amplitudes has received renewed attention in connection with the extended BvBMS symmetry [1,2,3,4,5,6]. In [14], the soft behaviour has been shown to be governed by the OPE of the vertex operators As a result both open and closed superstring amplitudes with external massless states expose the expected soft behaviour, while closed bosonic string amplitudes don’t, due to the tree-level non minimal coupling φR2 with the dilaton. We discuss the soft behaviour of open string amplitudes with gluons and massive states in any dimension and argue that the leading and sub-leading terms are universal and identical to the SYM case, relying on OPE and factorization. We check this explicitly for the amplitudes, we previously computed. Various appendices contain technical details that are included for completeness
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