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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 nonconservation 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 nontrivially 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. PACS:04.50.+ h;11.25.Mj. December 2004 † dp02@aub.edu.lb Introduction The hypothesis of the gauge-string correspondence, attempting to relate the gaugetheoretic and string degrees of freedom, is a long-standing problem of great importance. Remarkably, such a correspondence can be shown to occur both in the strongly coupled and the perturbative limits of Yang-Mills theory. Firstly, it is well-known that the AdS/CFT correspondence (e.g. see [1], [2], [3]) implies the isomorphism between vertex operators of string theory in the anti de Sitter backgrounds and the local gauge-invariant observables on the Yang-Mills side. On the other hand, recently it has been realized that some of the perturbative Yang-Mills scattering amplitudes are reproduced by the correlators of string theory with the twistorial target space and the related topological B-model with CalabiYau target space [4] The open string amplitudes of the twistor-string theory, supported on holomorphic curves in the projective space, have been shown to reproduce the perturbative gauge-theoretic ampludes and the perturbative expansion on the Yang-Mills side have been shown to correspond to the D-instanton (or the worldsheet instanton) expansion in string theory [5], [6]. Typically, the worldsheet correlators of twistorial string theory involve the GL(1)-neutral vertex operators from both open and closed sectors. As already has been noted, open string amplitudes reproduce the Yang-Mills perturbation theory, while the closed string modes describe the conformal supergravity in the low-energy limit [7], [8] In this letter, we show that, apart from the usual GL(1)-neutral operators, the twistor string theory also contains a set of physical GL(1)-charged vertex operators, argued to be related to the non-perturbative dynamics of the solitons appearing in conformal supergravity. These operators can be thought of as the second-quantized creation operators for the solitonic solutions of the conformal supergravity. Unfortunately, the precise form of these solutions in terms of the conformal supergravity fields remains undetermined in this paper and this is left for the future work. While these new vertex operators play no role in the MHV amplitudes, their role becomes important in the presence of the D-instantons (or, equivalently, in the non-MHV cases) and they do contribute nontrivially to both open and closed string amplitudes of the twistorial string theory. In this letter, we construct few examples of such GL(1)-charged BRST-invariant operators and derive the conditions for their BRST-invariance and non-triviality. At the first glance, appearance of such new physical vertices in twistor-string theory presents a problem as these states would seem to be in contradiction with the GL(1) gauge symmetry of the theory. One should remember, however, that in string theory BRST-invariance of some physical vertex operator does not automatically imply its gauge invariance. The simplest example is the local worldsheet