Alladi Ramakrishnan Hall

(Pre-synopsis seminar) Study of $Z_N$ Symmetry in SU(N) Gauge Theories in The Presence of Matter Fields.

Sabiar Shaikh

IMSc

Theoretical studies in Quantum Chromodynamics (QCD) show that at high
temperature hadrons melt into quark-gluon plasma (QGP) via a transition known as
confinement-deconfinement (CD) transition. In pure SU(N) gauge theories the CD
transition is described by the Polyakov loop and the $Z_N$ (center of SU(N))
symmetry. This symmetry is spontaneously broken in the deconfined phase. When
matter fields in the fundamental representation are included, the Euclidean action
breaks this symmetry explicitly. The non-perturbative studies have shown in
SU(2)-Higgs theory (scalar QCD) the partition function averages, in the continuum
limit (for large number of temporal sites ($N_\tau$)), exhibit the corresponding
$Z_2$ symmetry in parts of the phase diagram.
In this talk, we will discuss our work on the $Z_N$ symmetry in SU(N)-Higgs
theories. We present results of non-perturbative studies for $N=3$ which suggest
that, the $Z_3$ symmetry is effectively realized,in the Higgs symmetric phase. The
nature of the CD transition changes with $N_\tau$, becomes first order in the
continuum limit (as if in pure SU(N) theory). In the same limit, in the deconfined
phase the $Z_N$ states become degenerate.
To understand the realization of $Z_N$ symmetry, next we will discuss our study on
one dimensional gauged chain of matter fields. As in SU(N) gauge theories, the
action breaks $Z_N$ symmetry explicitly. The analytic calculation of the partition
function shows that the $Z_N$ symmetry is realized in the continuum limit for bosonic
matter fields. To further probe the reason behind the realisation of $Z_N$ symmetry
we consider a simple model of $Z_2$-Higgs theory in both 3+1 and 0+1 dimensions
where it is shown that the density of states (DoS) exhibits $Z_2$ symmetry. As DoS,
so entropy, dominate the thermodynamics (over the Boltzmann factor) in the Higgs
symmetric phase, the $Z_2$ symmetry is realized.