  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 beta-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 of Yang-Mills theory, they are shown to contribute
non-trivially to non-MHV correlators in the worldsheet instanton backgrounds.
We argue that these operators describe the non-perturbative dynamics of
solitons in conformal supergravity. However, the exact form of such solitonic
solutions is yet to be determined.
