On Integrability of Classical SuperStrings in AdS_5 x S^5

TL;DR

This work constructs a Lax representation for the classical AdS5×S5 superstring in a physical, light-cone gauge, focusing on the 8+8 physical degrees of freedom. By embedding the gauge-fixed equations into an su(2,2|4) matrix form, the authors obtain a Lax connection and a monodromy that demonstrate integrability on the physical subspace, while highlighting a fermionic Lambda term that alters the local curvature in the full algebra but not on psu(2,2|4). They perform explicit analyses in the AdS3×S3 and AdS3×S1 subsectors, deriving conserved charges and relating leading Lax asymptotics to global psu(2,2|4) generators and su(4) Dynkin labels. The results suggest that integrability persists in the physical theory and its supersymmetric subsectors, offering a path toward understanding quantum integrability and AdS/CFT connections. Future work includes extracting local integrals of motion from the Lax pair and clarifying the dual gauge-theory interpretation of the reduced sectors.

Abstract

We explore integrability properties of superstring equations of motion in AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding Hamiltonian dynamics on subspace of physical superstring degrees of freedom. We present some explicit results for the corresponding conserved charges by consistently reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both bosonic and fermionic fields.