After the proposal of Maldacena (AdS/CFT), there have been numerous attempts to find out gravity duals of various kinds of CFT. Klebanov and Polyakov gave one such correspondence here. The claim is this:
The singlet sector of the critical O(N) model with the (ϕaϕa)2 interaction is dual to the minimal bosonic theory in AdS4. Of course, we have to take the large N limit. Simplest such O(N) invariant theory (free, with no interactions) is:
S=12∫d3xN∑a=1(∂μϕa)2
How do I derive the conserved currents in this theory?
ϕa are
N-component vector fields and NOT
N×N matrix fields.
This post imported from StackExchange Physics at 2014-07-28 11:12 (UCT), posted by SE-user Debangshu