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

Abstract

This paper studies a special class of states for the dual conformal field theories associated with supersymmetric $Ad{S}_5\times X$ 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 $\mathcal{N}=4$ 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.

34 pages. v2: Improved discussion of three point functions in section 5. Fixed typos. Version accepted for publication in PRD

References in corpus (18)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• A Perturbative Window into Non-Perturbative Physics
• Magnon Bound States and the AdS/CFT Correspondence
• On lightcone string field theory from Super Yang-Mills and holography
• Kaluza-Klein Holography
• Normal random matrix ensemble as a growth problem
• Sasaki-Einstein Metrics on S^2 x S^3
• Anatomy of bubbling solutions
• Giant Gravitons - with Strings Attached (II)
• Dual Giant Gravitons in Sasaki-Einstein Backgrounds
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• Strings on conifolds from strong coupling dynamics, part I
• Rigid Holography and Six-Dimensional N=(2,0) Theories on AdS_5 times S^1
• Strings on conifolds from strong coupling dynamics: quantitative results
• ABJ(M) Chiral Primary Three-Point Function at Two-loops
• On the central charge extension of the N=4 SYM spin chain
• D-brane realizations of runaway behavior and moduli stabilization
• Commuting Quantum Matrix Models

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