$S_N$ Orbifolds and String Interactions

We study interacting features of $S_N$ Orbifold CFTs. Concentrating on characters (associated with $S_N$ Orbifold primaries) we first formulate a novel procedure for evaluating them through $GL(\infty)_+$ tracing. The result is a polynomial formula which we show gives results equivalent to those found by Bantay. From this we deduce a hierarchy of commuting Hamiltonians featuring locality in the induced space, and nonlinear string-type interactions.

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