Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra

TL;DR

This paper links extremal chiral ring states in AdS/CFT to free fermions and generalized oscillator algebras, revealing orthogonality of Schur functions and matching three-point functions with N=4 SYM, suggesting a fermionic description of these states.

Contribution

It introduces a novel fermionic framework for extremal chiral ring states in AdS/CFT using a generalized oscillator algebra, extending previous models.

Findings

Extremal chiral ring states correspond to multitraces and Schur functions of a composite field.

Orthogonality of Schur functions in the zero coupling limit.

Three-point functions match N=4 SYM results up to normalization.

Abstract

This paper studies a special class of states for the dual conformal field theories associated with supersymmetric $AdS_5\times X$ 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 ${\cal 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 K\"ahler potential on this subset of the moduli space.