Speaker
Description
Abstract: we study the confinement-deconfinement transition and $Z_2$ symmetry in lattice $Z_2+$Higgs theory in $3+1$ dimensional Euclidean space using lattice Monte Carlo simulation methods. In pure $Z_2$ gauge theory the CD transition is first order. Polyakov loop acquires non-zero thermal average value in the deconfined phase and the $Z_2$ symmetry is spontaneously broken. The $Z_2$ symmetry arises from the fact that the allowed gauge transformations are either periodic or anti-periodic in the temporal direction. In the presence of matter fields in the fundamental representation, only the periodic gauge transformations are allowed. Though the action is invariant under anti-periodic gauge transformations, the gauge transformed matter fields do not satisfy required boundary conditions. A configuration of the Polyakov loop and it's $Z_2$ rotated counter part do not have same action, resulting in the explicit breaking of $Z_2$ symmetry. Using numerical Monte Carlo simulations, we compute physical observable sensitive to $Z_2$ symmetry, in order to study the strength of this explicit breaking in the phase diagram of the theory.
Our results shows that this $Z_2$ symmetry is realised in the Higgs symmetric phase for large number of temporal lattice sites. Though the action does not have $Z_2$ symmetry but partition function averages exhibit $Z_2$ symmetry for large number of temporal sites. We also observe that the $Z_2$ symmetry is
badly broken in the Higgs broken phase and the strength of the explicit symmetry breaking decreases on approach towards the Higgs symmetric phase. To understand the dependence of $Z_2$ symmetry on the number of temporal sites, we consider a simple one dimensional model keeping terms of the original action corresponding to a single spatial site. The partition function and the corresponding free
energy for each of the two Polyakov loop sectors are calculated exactly. It is observed that the free energy difference between the two Polyakov loop sectors vanishes in the large temporal lattice sites, which leads to $Z_2$ symmetry. We argue that this is due to the dominance of entropy or the distribution of the density of states corresponding to the action.
