= Single-trace operator
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A single-trace operator contains one <trace> over matrix-valued <gauge group> indices. For adjoint matrix fields, $\operatorname{Tr}(\Phi^2)$ is a simple example, whereas $\operatorname{Tr}(\Phi^2)\operatorname{Tr}(\Phi^3)$ is a multi-trace product. The trace makes these expressions invariant under simultaneous conjugation by the <gauge group>.
In a suitable large-rank holographic theory, normalized single-trace operators correspond at leading order to single-particle bulk excitations, while multi-trace products create multiparticle states. This is an additional dynamical interpretation, rather than the definition of taking one trace. Mixing and finite-rank trace identities qualify the separation beyond the ideal large-rank limit. The distinction organizes <correlation function> counting and the bulk field content in <AdS CFT correspondence>.
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