CFT representation of interacting bulk gauge fields in AdS
Abstract
We develop the representation of interacting bulk gauge fields and charged scalar matter in antide Sitter in terms of nonlocal observables in the dual conformal field theory (CFT). We work in the holographic gauge in the bulk, A_{z}=0. The correct statement of microcausality in the holographic gauge is somewhat subtle, so we first discuss it from the bulk point of view. We then show that in the 1/N expansion, CFT correlators can be lifted to obtain bulk correlation functions that satisfy microcausality. This requires adding an infinite tower of higherdimension multitrace operators to the CFT definition of a bulk observable. For conserved currents, the Ward identities in the CFT prevent the construction of truly local bulk operators (i.e., operators that commute at spacelike separation with everything); however, the resulting nonlocal commutators are exactly those required by the bulk Gauss constraint. In contrast, a CFT which only has nonconserved currents can be lifted to a bulk theory which is truly local. Although our explicit calculations are for gauge theory, similar statements should hold for gravity.
 Publication:

Physical Review D
 Pub Date:
 April 2013
 DOI:
 10.1103/PhysRevD.87.086004
 arXiv:
 arXiv:1212.3788
 Bibcode:
 2013PhRvD..87h6004K
 Keywords:

 11.25.Tq;
 04.60.Cf;
 Gauge/string duality;
 Gravitational aspects of string theory;
 High Energy Physics  Theory
 EPrint:
 34 pages. v2: minor edits, version to appear in PRD