Test of a two-level algorithm for the glueball spectrum in $SU(N_c)$ Yang-Mills theory

TL;DR

This paper introduces a new two-level sampling algorithm for calculating the glueball spectrum in $SU(N_c)$ Yang-Mills theory, demonstrating its performance and initial results for low-lying states at $N_c=3$.

Contribution

The paper presents a novel two-level sampling method for glueball correlators and a new code capable of constructing and classifying loop operators of various shapes.

Findings

Algorithm shows promising performance in computing glueball states.

Initial results for low-lying glueball spectrum at $N_c=3$ are consistent with existing literature.

The code efficiently classifies operators according to cubic group representations.

Abstract

We present preliminary results obtained using a new code for $SU (N_c)$ Yang-Mills theory which performs a 2-level sampling of glueball correlators obtained from a suitably chosen basis of (APE) smeared and unsmeared operators. The code builds loop operators of any shape and length and classifies them according to the irreducible representations of the cubic group. We report on the performances of the algorithm and on the computation of the first low-lying glueball states choosing $N_c = 3$ as a reference to compare our results with the literature.