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.
Highlights
The AdS/CFT correspondence [1] suggests that there should be a relation between the low energy effective field theories of string theory or M-theory on AdS spaces and the dual gauge theory
It is expected that in order for local physics to work, a gap in anomalous dimensions develops [6] and that one can count constraints arising from crossing symmetry in correlators and match them to polynomial terms in the AdS effective action
One can argue that this approach shows that effective field theory in the bulk makes sense from the point of view of field theory constructions on the boundary. This setup has not furnished a proof of locality. It doesn’t explain what happens when the conformal symmetry of the bulk is broken, and local physics on AdS5 × S5 is not the same as local physics on AdS: one can have scattering into the sphere directions from wave packets starting in AdS
Summary
The AdS/CFT correspondence [1] suggests that there should be a relation between the low energy effective field theories of string theory (both with open and closed strings) or M-theory on AdS spaces and the dual gauge theory. To address the problem of the position of the brane in the AdS geometry directly from field theory, one needs to find a collective coordinate that parametrizes generalized coherent states which permit a geometric interpretation of the position of the D-brane as a specific value of this collective coordinate Given two such D-brane excitations of the geometry we can in principle start studying the spectrum of strings stretching between them and in this way obtain metric information about the geometry in which they live. We generalize from these observations what the higher loop result should look like to all orders.
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