$S_N$ Orbifolds and String Interactions

TL;DR

This paper develops a new polynomial method for evaluating characters in $S_N$ Orbifold CFTs, revealing a hierarchy of commuting Hamiltonians with string-like interactions.

Contribution

Introduces a novel polynomial formula for characters in $S_N$ Orbifold CFTs and uncovers a hierarchy of local, nonlinear string interactions.

Findings

Polynomial formula matches Bantay's results

Hierarchy of commuting Hamiltonians identified

String-type interactions characterized

Abstract

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.