The Yang-Mills Spectrum from a 2-level Algorithm

TL;DR

This paper introduces a 2-level algorithm for computing 2-point functions in lattice gauge theory, demonstrating significant CPU time reductions for glueball mass calculations in 2+1D SU(2) gluodynamics, especially for heavier states.

Contribution

The paper presents a novel 2-level algorithm optimized for lattice gauge theory computations, improving efficiency in calculating glueball masses across different dimensions and gauge groups.

Findings

CPU time reduction between 1.5 and 7 times for lightest glueballs

Efficiency gain increases exponentially with mass and time separation

Algorithm effective across multiple dimensions and gauge groups

Abstract

We investigate in detail a 2-level algorithm for the computation of 2-point functions of fuzzy Wilson loops in lattice gauge theory. Its performance and the optimization of its parameters are described in the context of 2+1D SU(2) gluodynamics. In realistic calculations of glueball masses, it is found that the reduction in CPU time for given error bars on the correlator at time-separation ~0.2fm, where a mass-plateau sets in, varies between 1.5 and 7 for the lightest glueballs in the non-trivial symmetry channels; only for the lightest glueball is the 2-level algorithm not helpful. For the heavier states, or for larger time-separations, the gain increases as expected exponentially in (mt). We present further physics applications in 2+1 and 3+1 dimensions and for different gauge groups that confirm these conclusions.