Soft theorem for the graviton, dilaton and the Kalb-Ramond field in the bosonic string

Abstract

We study the behavior of the scattering amplitudes of the bosonic string involving a soft massless state (graviton, dilaton and Kalb-Ramond antisymmetric tensor) and closed string tachyons or other closed string massless states. For a soft graviton we confirm the results, obtained in Ref. [24] using just gauge invariance, up to terms of $\mathcal{O}(q^1)$ for external tachyons and up to terms of $\mathcal{O}(q^0)$ for external massless closed string states. Furthermore, we also derive the behavior of the scattering amplitude when a dilaton or a Kalb-Ramond field becomes soft. These results are new and cannot, to our knowledge, be derived by using gauge invariance. It turns out, in the cases examined, that the soft amplitude for a dilaton or for an antisymmetric tensor is obtained by saturating the tensor, $M_{\mu \nu }$, derived from gauge invariance for gravitons, with their respective polarization tensors. Thus extra terms that could have appeared in $M_{\mu \nu }$ in the case of a soft dilaton, in fact do not appear.

17 pages + 10 pages Appendix. Several clarifying comments added in this version

References in corpus (12)

• New Relations for Gauge-Theory Amplitudes
• Evidence for a New Soft Graviton Theorem
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Soft sub-leading divergences in Yang-Mills amplitudes
• Subleading Soft Factor for String Disk Amplitudes
• Soft Graviton Theorem in Arbitrary Dimensions
• Conformal Invariance of the Subleading Soft Theorem in Gauge Theory
• Factorized soft graviton theorems at loop level
• Soft Theorems from Effective Field Theory
• A Note on Soft Factors for Closed String Scattering

Cited by in corpus (6)

• Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton
• The B-field soft theorem and its unification with the graviton and dilaton
• String Memories ... openly retold
• Spinning-off stringy electro-magnetic memories
• Soft gravitational radiation from multi-body collisions
• S-matrix element of two R-R and one NS states