Fluctuations, Topological Defects and Metastable states [HBNI Th270]

Abstract

This thesis consists of three parts. In first, we will examine the validity of the geodesic rule, a key postulate of the Kibble-Zurek mechanism, which describes topological defect formation during second-order phase transitions. Using equilibrium Monte Carlo simulations of the XY model and a complex scalar field theory, we find that thermal fluctuations cause a breakdown of the geodesic rule, leading to a higher defect density than standard predictions. The second part explores how spacetime oscillations affect fluctuations in non-Abelian SU(2) gauge fields. Oscillatory terms in the metric enter the evolution equations, generating resonance in field fluctuations. Initially, when fluctuations are small and terms nonlinear in gauge fields can be ignored, the dynamics similar to U(1) gauge fields. In this linear regime, field modes exhibit parametric resonance. However, as non-Abelian effects emerge, SU(2) gauge fields show enhanced growth, leading to increased energy density and tr(FF˜). Finally, we will discuss Z3 symmetry in 2+1 flavor QCD. The presence of dynamical fermions break the Z3 symmetry explicitly. Consequently, in the deconfined phase two meta-stable states appear for high enough temperatures. Our preliminary results suggest that these states may be present for temperatures(370MeV< Tm ≤ 446MeV) achieved in Heavy-ion collision experiments