Classical Open String Integrability

TL;DR

This paper develops a method to construct conserved charges for classical open strings on coset spaces, applying it to various boundary conditions in AdS/CFT setups, revealing integrability properties and limitations.

Contribution

Introduces a simple procedure using reflection matrices to construct non-local conserved charges for classical open strings, analyzing their existence under different boundary conditions.

Findings

Conserved charges are constructible for maximal Giant Gravitons and D7-branes.

Charges are only constructible in an SU(2) subsector for D5-branes.

No conserved charges can be constructed for non-maximal Giant Gravitons.

Abstract

We present a simple procedure to construct non-local conserved charges for classical open strings on coset spaces. This is done by including suitable reflection matrices on the classical transfer matrix. The reflection matrices must obey certain conditions for the charges to be conserved and in involution. We then study bosonic open strings on $AdS_5\times S^5$. We consider boundary conditions corresponding to Giant Gravitons on $S^5$, $AdS_4\times S^2$ D5-branes and $AdS_5 \times S^3$ D7-branes. We find that we can construct the conserved charges for the full bosonic string on a Maximal Giant Graviton or a D7-brane. For the D5-brane, we find that this is possible only in a SU(2) sub-sector of the open string. Moreover, the charges can not be constructed at all for non-maximal Giant Gravitons. We discuss the interpretation of these results in terms of the dual gauge theory spin chains.