Hidden Symmetries of the AdS_5 x S^5 Superstring

TL;DR

The paper tackles how to access solvable structures in the string worldsheet for RR backgrounds by exploring hidden symmetries. It demonstrates that the Green-Schwarz string on $AdS_5 \times S^5$ possesses an infinite set of nonlocal, classically conserved charges arising from a one-parameter family of flat connections, signaling classical integrability, and extends the discussion to related backgrounds. It also investigates local higher-spin currents, finding no nontrivial examples in the full theory, though the conformal gauge hints at sectoral simplifications. The work motivates applying integrable-field-theory techniques to the AdS/CFT context and outlines future steps toward quantization, Poisson-bracket structure, and broader AdS backgrounds.

Abstract

Attempts to solve Yang-Mills theory must eventually face the problem of analyzing the theory at intermediate values of the coupling constant. In this regime neither perturbation theory nor the gravity dual are adequate, and one must consider the full string theory in the appropriate background. We suggest that in some nontrivial cases the world sheet theory may be exactly solvable. For the Green-Schwarz superstring on AdS_5 x S^5 we find an infinite set of nonlocal classically conserved charges, of the type that exist in integrable field theories.