Conformal Affine Toda Soliton and Moduli of IIB Superstring on $AdS_5\times S^5$

TL;DR

This paper explores the hidden affine symmetry in the moduli space of IIB superstring theory on AdS5×S5, linking it to conformal affine Toda models and twistor space, revealing new geometric and algebraic structures.

Contribution

It introduces a novel interpretation of the superstring moduli space via affine Toda models and elucidates the role of affine symmetry and twistor geometry in this context.

Findings

Identification of the moduli space with conformal affine Toda models.

Connection between poles in Riemann-Hilbert problems and superstring moduli.

Affine SU(4) symmetry extends conformal symmetry in twistor space.

Abstract

In this paper we interpret the hidden symmetry of the moduli space of IIB superstring on $AdS_{5}\times S^{5}$ in terms of the chiral embedding in $AdS_{5}$, 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.