Extremal chiral ring states in the AdS/CFT correspondence are described by free fermions for a generalized oscillator algebra
This paper studies a special class of states for the dual conformal field theories associated with supersymmetric AdS5×X compactifications, where X is a Sasaki-Einstein manifold with additional U (1 ) symmetries. Under appropriate circumstances, it is found that elements of the chiral ring that maximize the additional U (1 ) charge at fixed R-charge are in one to one correspondence with multitraces of a single composite field. This is also equivalent to Schur functions of the composite field. It is argued that in the formal zero coupling limit that these dual field theories have, the different Schur functions are orthogonal. Together with large N counting arguments, one predicts that various extremal three point functions are identical to those of N =4 SYM, except for a single normalization factor, which can be argued to be related to the R-charge of the composite word. The leading and subleading terms in 1 /N are consistent with a system of free fermions for a generalized oscillator algebra. One can further test this conjecture by constructing coherent states for the generalized oscillator algebra that can be interpreted as branes exploring a subset of the moduli space of the field theory and use these to compute the effective Kähler potential on this subset of the moduli space.
Physical Review D
- Pub Date:
- August 2015
- Gauge/string duality;
- High Energy Physics - Theory
- 34 pages. v2: Improved discussion of three point functions in section 5. Fixed typos. Version accepted for publication in PRD