Anomalous dimensions in the symmetric orbifold

TL;DR

This paper confirms previous results on anomalous dimensions in symmetric orbifolds through direct calculations and introduces new techniques and a Mathematica code for analyzing BPS states at finite cycle lengths.

Contribution

It provides a direct perturbed 2-point function calculation method and develops tools for analyzing arbitrary quarter BPS states in symmetric orbifolds.

Findings

Reproduced known anomalous dimension results from direct calculations.

Developed techniques and code for finite cycle length BPS state analysis.

Validated dispersion relations for torus magnons in the large-w limit.

Abstract

Recently, the anomalous conformal dimensions of the symmetric orbifold under the $2$-cycle twisted sector deformation were calculated using the perturbed action of the supercharges. In particular, explicit and simple formulae for the dispersion relations of the torus magnons in the $w$-cycle twisted sector were derived for large $w$. In this paper we reproduce these results from a direct perturbed $2$-point function calculation. In the process we also develop techniques (and a Mathematica code) that allows one to do these calculations for arbitrary quarter BPS states at finite $w$.