Conformal Affine Toda Soliton and Moduli of IIB Superstring on $Ad{S}_5\times S^5$

Abstract

In this paper we interpret the hidden symmetry of the moduli space of IIB superstring on $Ad{S}_5\times S^5$ in terms of the chiral embedding in $Ad{S}_5$, which turns to be the ${\mathbb{CP}}^3$ conformal affine Toda model. We review how the position $\mu$ of poles in the Riemann-Hilbert formulation of dressing transformation and how the value of loop parameters $\mu$ in the vertex operator of affine algebra determines the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinize the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients $\mu$ of twistor.

Final version, Misprints corrected, Note added

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