• Yang-Mills
• lattice QCD
• QCD
• trace deformation
• topology
• phase diagram
• compactification

Due to asymptotic freedom, high energy phenomena of QCD and Yang-Mills theories can be studied by means of perturbation theory. Low energy properties, such as hadron phenomenology and confinement cannot be reached by perturbative methods because the coupling strength rises at low energies.

It has been proposed by Eguchi and Kawai that Yang-Mills theory on a finite volume does not depend on the volume, and that it is equivalent to a single-site matrix model. However, volume independence only holds until the length of one of the dimensions becomes smaller than a critical compactification length, under which center symmetry is spontaneously broken.

Compactifying one dimension to a length L introduces an energy scale ~1/L, which means that at small compactification lengths semiclassical methods can be used to study the theory. However, center symmetry breaking is related to the deconfinement transition, and this only gives us information on the deconfined phase. It has been proposed by Ünsal and Yaffe that by adding trace deformation terms to the action, center symmetry can be recovered at arbitrarily small L, potentially enabling a semiclassical study of non-perturbative phenomena.

In this work, SU(3) Yang-Mills theory with a double compactification (T^2 \times R^2) is studied by means of Monte Carlo methods. In particular, the phase diagram of the theory and topological properties have been explored. The impact of trace deformation terms on symmetry realization, topological properties and the UV structure of the theory have been examined.