Bosonic sectorized strings and the $(DF)^{2}$ theory

In this work, we investigate the bosonic chiral string in the sectorized interpretation, computing its spectrum, kinetic action and $3$-point amplitudes. As expected, the bosonic ambitwistor string is recovered in the tensionless limit. We also consider an extension of the bosonic model with current algebras. In that case, we compute the effective action and show that it is essentially the same as the action of the mass-deformed $(DF)^{2}$ theory found by Johansson and Nohle. Aspects which might seem somewhat contrived in the original construction --- such as the inclusion of a scalar transforming in some real representation of the gauge group --- are shown to follow very naturally from the worldsheet formulation of the theory.