The Affine Hidden Symmetry and Integrability of Type IIB Superstring in $Ad{S}_5\times S^5$

Abstract

In this paper, we motivate how the Hodge dual related with S-duality gives the hidden symmetry in the moduli space of IIB string. Utilizing the static -symmetric Killing gauge, if we take the Hodge dual of the vierbeins keeping the connection invariant, the duality of Maure-Cartan equations and the equations of motion becomes manifest. Thus by twistly transforming the vierbein, we can express the BPR currents as the Lax connections by a unique spectral parameter. Then we construct the generators of the infinitesimal dressing symmetry, the related symmetric algebra becomes the affine , which can be used to find the classical $r$ matrix.

arXiv comment16 pages, no figures,typo crrected and references added

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• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Super-Poincare Covariant Quantization of the Superstring
• Mirror Manifolds And Topological Field Theory
• Spin chains and string theory
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• Classical Integrability and Super Yangian of Superstring on AdS_5 x S^5
• Affine A^{(1)}_{3} N=2 monopole as the D module and affine ADHMN sheaf