SO(N) restricted Schur polynomials

TL;DR

This paper constructs an orthogonal basis of gauge-invariant operators in the 1/4-BPS sector of SO(N) super Yang-Mills theory, facilitating the study of giant graviton dynamics and their dual string theory descriptions.

Contribution

It provides an explicit construction and exact evaluation of two-point functions for restricted Schur polynomials in the SO(N) gauge theory, matching state counting with Young diagram labels.

Findings

Matching of state counting and Young diagram classification.

Explicit construction of gauge-invariant operators.

Exact evaluation of two-point functions.

Abstract

We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT dual in the form of type IIB string theory with AdS_5 X RP^5 geometry. With the aim of studying excited giant graviton dynamics, we construct an orthogonal basis for this sector of the gauge theory in this work. First, we demonstrate that the counting of states, as given by the partition function, and the counting of restricted Schur polynomials matches by restricting to a particular class of Young diagram labels. We then give an explicit construction of these gauge invariant operators and evaluate their two-point function exactly. This paves the way to studying the spectral problem of these operators and their D-brane duals.