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

Bo-Yu Hou·Dan-Tao Peng·Chuan-Hua Xiong·Rui-Hong Yue
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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 $% κ$-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 $% gl(2,2|4)^{(1)}$, which can be used to find the classical $r$ matrix.

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Bo-Yu Hou, Dan-Tao Peng, Chuan-Hua Xiong, Rui-Hong Yue. 2004-07-08. The Affine Hidden Symmetry and Integrability of Type IIB Superstring in $AdS_{5} \times S^{5}$. https://arxiv.org/abs/hep-th/0406239

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