Restricted Schurs and correlators for SO(N) and Sp(N)
Garreth Kemp
TL;DR
This paper extends the use of restricted Schur polynomials to Sp(N) gauge theories, providing exact methods to compute correlation functions of multi-trace operators in free N=4 super Yang-Mills with SO(N) and Sp(N) gauge groups.
Contribution
It introduces a new framework for constructing gauge-invariant operators in Sp(N) theories and develops exact correlation function computation techniques for these operators.
Findings
Restricted Schur polynomials form a complete orthogonal basis for SO(N) and Sp(N) gauge theories.
Exact correlation functions of multi-trace operators with two scalars are derived.
The methods generalize previous results from SO(N) to Sp(N) gauge groups.
Abstract
In a recent work, restricted Schur polynomials have been argued to form a complete orthogonal set of gauge invariant operators for the 1/4-BPS sector of free N = 4 super Yang-Mills theory with an SO(N) gauge group. In this work, we extend these results to the theory with an Sp(N) gauge group. Using these operators, we develop techniques to compute correlation functions of any multi-trace operators with two scalar fields exactly in the free theory limit for both SO(N) and Sp(N).
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