TL;DR
This paper constructs new infinite sets of commuting charges in a broad class of conformal field theories, revealing a unified structure across different gauge groups and highlighting the special role of restricted Schur polynomials.
Contribution
It introduces a unified framework for constructing commuting charges in various gauge theories using Lie algebra embeddings, emphasizing the significance of restricted Schur polynomials.
Findings
Eigenstates are restricted Schur polynomials.
Eigenvalues encode correlator values of restricted Schurs.
Charges distinguish restricted Schurs among other bases.
Abstract
In this paper we construct two infinite sets of self-adjoint commuting charges for a quite general CFT. They come out naturally by considering an infinite embedding chain of Lie algebras, an underlying structure that share all theories with gauge groups U(N), SO(N) and Sp(N). The generality of the construction allows us to carry all gauge groups at the same time in a unified framework, and so to understand the similarities among them. The eigenstates of these charges are restricted Schur polynomials and their eigenvalues encode the value of the correlators of two restricted Schurs. The existence of these charges singles out restricted Schur polynomials among the number of bases of orthogonal gauge invariant operators that are available in the literature.
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