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Starting from the amplitude with an arbitrary number of massless closedstates of the bosonic string, we compute the soft limit when one of the statesbecomes soft to subsubleading order in the soft momentum expansion, and we showthat when the soft state is a graviton or a dilaton, the full string amplitudecan be expressed as a soft theorem through subsubleading order. It turns outthat there are string corrections to the field theoretical limit in the case ofa soft graviton, while for a soft dilaton the string corrections vanish. Wethen show that the new soft theorems, including the string corrections, can besimply obtained from the exchange diagrams where the soft state is attached tothe other external states through the three-point string vertex of threemassless states. In the soft-limit, the propagator of the exchanged state isdivergent, and at tree-level these are the only divergent contributions to thefull amplitude. However, they do not form a gauge invariant subset and must besupplemented with extra non-singular terms. The requirement of gauge invariancethen fixes the complete amplitude through subsubleading order in the softexpansion, reproducing exactly what one gets from the explicit calculation instring theory. From this it is seen that the string corrections atsubsubleading order arise as a consequence of the three-point amplitude havingstring corrections in the bosonic string. When specialized to a soft dilaton,it remarkably turns out that the string corrections vanish and that thenon-singular piece of the subsubleading term of the dilaton soft theorem is thegenerator of space-time special conformal transformation.

Subsubleading soft theorems of gravitons and dilatons in the bosonic string