Restricted Schur Polynomials for Fermions and integrability in the su(2|3) sector

TL;DR

This paper introduces restricted Schur polynomials combining fermionic and bosonic fields, diagonalizes the one-loop dilatation operator in the su(2|3) sector, and reveals integrable structures in non-planar large N limits.

Contribution

It defines new restricted Schur polynomials for fermions and bosons, and demonstrates their diagonalization of the one-loop dilatation operator in the su(2|3) sector using a double coset ansatz.

Findings

Operators diagonalize the free field two-point function to all orders in 1/N.

Spectrum of anomalous dimensions matches decoupled oscillators.

Diagonalization applies to both su(2|3) and sl(2) sectors.

Abstract

We define restricted Schur polynomials built using both fermionic and bosonic fields which transform in the adjoint of the gauge group U(N). We show that these operators diagonalize the free field two point function to all orders in 1/N. As an application of our new operators, we study the action of the one loop dilatation operator in the su(2|3) sector in a large N but non-planar limit. The restricted Schur polynomials we study are dual to giant gravitons. We find that the one loop dilatation operator can be diagonalized using a double coset ansatz. The resulting spectrum of anomalous dimensions matches the spectrum of a set of decoupled oscillators. Finally, in an Appendix we study the action of the one loop dilatation operator in an sl(2) sector. This action is again diagonalized by a double coset ansatz.