Classical open string integrability

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 ×S 5 . We consider boundary conditions corresponding to Giant Gravitons on S 5 , AdS 4 × S 2 D5-branes and AdS 5 × 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.

Integrable open spin chains from flavored ABJM theory

“…For the four dimensional case considered in [7], as far as we know, there are no higher loop computations in the gauge theory side to obtain the higher order Hamiltonian and check the integrability at higher loop order. In the dual open string theory side, strong evidence for the integrability of the classical worldsheet theory was obtained in [33] by constructing non-local conserved charges in the full bosonic sector. This suggested that the field theory in the planar limit is integrable in the strong coupling regime.…”

Reflecting magnons from D7 and D5 branes

“…and which is solved only by using the mass-shell condition (29) and in addition imposing the equation…”

ASPECTS OF INTEGRABILITY IN $\mathcal{N} = 4$ SYM

“…Evidence for classical open string integrability in the giant graviton background, from the world-sheet point of view has also recently been presented in [28]. For a detailed analysis of various other recently discovered aspects of open string dynamics and their gauge theory duals we shall refer to [27].…”