Spectrum of Trace Deformed Yang-Mills Theories

TL;DR

This study uses numerical simulations to analyze how trace deformation affects the scalar glueball mass and torelon ground state in Yang-Mills theories on , revealing stability of glueball mass and complex torelon behavior.

Contribution

It provides the first numerical investigation of glueball and torelon properties in trace deformed Yang-Mills theories, linking deformation parameters to effective compactification size.

Findings

Glueball mass remains stable across different compactification radii.

Torelon ground state exhibits a plateau at large deformation strength.

Results suggest partial agreement with large- predictions.

Abstract

In this paper we study, by means of numerical simulations, the behaviour of the scalar glueball mass and the ground state of the torelon for trace deformed Yang-Mills theory defined on $ \mathbb{R}^3\times S^1$, in which center symmetry is recovered even at small compactification radii. We find, by investigating both $SU(3)$ and $SU(4)$ pure gauge theories, that the glueball mass computed in the deformed theory, when center symmetry is recovered, is compatible with its value at zero temperature and does not show any significant dependence on the compactification radius; moreover, we establish a connection between the deformation parameter and an effective compactification size, which works well at least for small deformations. In addition, we observe that the ground state of the torelon which winds around the small traced deformed circle with size $l$ acquires a pleateau for large values of the strength $h$, with values which are compatible with a $1/l$ behavior but, on the other hand, are still not in complete agreement with the asymptotic semiclassical large-$N$ predictions.