The Algebra of Transition Matrices for the AdS_5 x S^5 Superstring

TL;DR

This paper explores the integrability of the superstring on AdS_5 x S^5, introducing a new family of currents, analyzing the Hamiltonian structure, and generalizing automorphisms to deepen understanding of its mathematical properties.

Contribution

It constructs a new one-parameter family of currents satisfying the zero curvature condition and generalizes the  automorphism for the AdS_5 x S^5 superstring.

Findings

Constructed a new family of flat currents.

Analyzed the Poisson algebra of transition matrices.

Generalized the  automorphism for the model.

Abstract

We consider integrability properties of the superstring on $AdS_{5}\times S^{5}$ background and construct a new one parameter family of currents which satisfies the vanishing curvature condition. We present the Hamiltonian analysis for the sigma model action and determine the Poisson algebra of the transition matrices. We reveal the generalization of the $\mathbb{Z}_{4}$ automorphism analogous to the sigma models defined on a symmetric space coset. A possible regularization scheme for the ambiguities present, which respects the generalized automorphism, is also discussed.