Open spin chains for giant gravitons and relativity

Abstract

We study open spin chains for strings stretched between giant graviton states in the N=4 SYM field theory in the collective coordinate approach. We study the boundary conditions and the effective Hamiltonian of the corresponding spin chain to two loop order. The ground states of the spin chain have energies that match the relativistic dispersion relation characteristic of massive W boson particles on the worldvolume of the giant graviton configurations, up to second order in the limit where the momentum is much larger than the mass. We find evidence for a non-renormalization theorem for the ground state wave function of this spin chain system. We also conjecture a generalization of this result to all loop orders which makes it compatible with a fully relativistic dispersion relation. We show that the conjecture follows if one assumes that the spin chain admits a central charge extension that is sourced by the giant gravitons, generalizing the giant magnon dispersion relation for closed string excitations. This provides evidence for ten dimensional local physics mixing AdS directions and the five-sphere emerging from an N=4 SYM computation in the presence of a non-trivial background (made of D-branes) that break the conformal field theory of the system.