Non-local charges on AdS_5 x S^5 and PP-waves

TL;DR

The paper investigates infinite families of nonlocal classically conserved charges for the Green-Schwarz superstring on pp-wave backgrounds and connects them to the well-known charges on $AdS_5\times S^5$ via the Penrose limit. It develops two complementary constructions: a direct pp-wave sigma-model approach using a nondegenerate invariant to build nontrivial charges, and a Penrose-limit derivation from the AdS$_5\times S^5$ charges, showing agreement at the first nontrivial order. The authors provide explicit expressions for the first and second nonlocal charges on the pp-wave, including their oscillator representations, and demonstrate a concrete semiclassical check against BMN-like states by matching the AdS$_5\times S^5$ charge $Q^3_{AdS}$ to the pp-wave charge $Q_3^{NT}$ in the large-$J$ limit. They discuss the implications for integrability in the closed-string, periodically-bounded case and highlight open questions, such as fermionic extensions and fully generating the infinite tower. Overall, the work clarifies how nonlocal conserved charges in the pp-wave limit reflect and illuminate the integrable structure of strings in $AdS_5\times S^5$.

Abstract

We show the existence of an infinite set of non-local classically conserved charges on the Green-Schwarz closed superstring in a pp-wave background. We find that these charges agree with the Penrose limit of non-local classically conserved charges recently found for the $AdS_5 \times S^5$ Green-Schwarz superstring. The charges constructed in this paper could help to understand the role played by these on the full $AdS_5 \times S^5$ background.