GL(1) charged states in twistor string theory

We discuss the appearance of the GL(1) charged physical operators in the twistor string theory. These operators are shown to be BRST-invariant and non-trivial and some of their correlators and conformal β-functions are computed. Remarkably, the non-conservation of the GL(1) charge in interactions involving these operators, is related to the anomalous term in the Kac-Moody current algebra. While these operators play no role in the maximum helicity violating (MHV) amplitudes, they are shown to contribute non-trivially to the non-MHV correlators in the presence of the worldsheet instantons. We argue that these operators describe the non-perturbative dynamics of solitons in conformal supergravity. The exact form of such solitonic solutions is yet to be determined.