Rotating restricted Schur polynomials

Abstract

Large N but non-planar limits of N = 4 super Yang-Mills theory can be described using restricted Schur polynomials. Previous investigations demonstrate that the action of the one loop dilatation operator on restricted Schur operators, with classical dimension of order N and belonging to the su(2) sector, is largely determined by the su(2) R symmetry algebra as well as structural features of perturbative field theory. Studies presented so far have used the form of R symmetry generators when acting on small perturbations of half-BPS operators. In this article, as a first step towards going beyond small perturbations of the half-BPS operators, we explain how the exact action of symmetry generators on restricted Schur polynomials can be determined.

Permutations and the combinatorics of gauge invariants for general $N$

“…I have described a body of techniques based on permutations and diagrams to approach problems of enumerating gauge invariants and computing correlators in 1-matrix models, multi-matrix models, quiver gauge theories and tensor models. They are also useful in computing the spectrum of loop-corrected dilatation operators, particularly in the sector of perturbations around half-BPS giant gravitons ( see [29,30,31,32,33] and references therein). Some progress has been made in finding the general quarter or eighth BPS ground states, which are ground states of the 1-loop dilatation operator acting on holomorphic invariants built from two or three complex matrices [34,35].…”

Central charges for the double coset

“…In this appendix we review results that were obtained in [42]. We would like to obtain the action of the following su(2) R generators…”

“…In the distant corners approximation, the computation of the traces that need to be computed is reduced to the evaluation of su(2) Clebsch-Gordan coefficients. The result is [42] Tr…”

Central Charges for the Double Coset

“…In this Appendix we review results that were obtained in [41]. We would like to obtain the action of the following su(2) R generators…”

“…In the distant corners approximation, the computation of the traces that need to be computed is reduced to the evaluation of su(2) Clebsch-Gordan coefficients. The result is [41] Tr X d dY O…”