Relation between large dimension operators and oscillator algebra of Young diagrams

Abstract

The operators with large scaling dimensions can be labelled by Young diagrams. Among other bases, the operators using restricted Schur polynomials have been known to have a large $N$ but nonplanar limit under which they map to states of a system of harmonic oscillators. We analyze the oscillator algebra acting on pairs of long rows or long columns in the Young diagrams of the operators. The oscillator algebra can be reached by a Inonu-Wigner contraction of the $u(2)$ algebra inside of the $u(p)$ algebra of $p$ giant gravitons. We present evidences that integrability in this case can persist at higher loops due to the presence of the oscillator algebra which is expected to be robust under loop corrections in the nonplanar large $N$ limit.

21 pages

References in corpus (6)

• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Nonplanar Integrability
• A study of open strings ending on giant gravitons, spin chains and integrability
• Surprisingly Simple Spectra
• Higher Loop Nonplanar Anomalous Dimensions from Symmetry

Cited by in corpus (8)

• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Anomalous Dimensions of Heavy Operators from Magnon Energies
• Central Charges for the Double Coset
• Negative anomalous dimensions in N=4 SYM
• Generating Functions for Giant Graviton Bound States
• Oscillating Multiple Giants
• Heavy Operators in Superconformal Chern-Simons Theory
• Interacting Emergent Yang-Mills theory