Spectrum of trace deformed Yang-Mills theories

In this paper we study, by means of numerical simulations, the behavior of the scalar glueball mass and the ground state of the torelon for trace deformed Yang-Mills theory defined on ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$, 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 plateau 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.