Formation of Topological Defects with Explicit Symmetry Breaking

Abstract

We demonstrate a novel mechanism for the formation of topological defects in a first order phase transition for theories in the presence of small explicit symmetry breaking terms. We carry out numerical simulations of collisions of two bubbles in 2+1 dimensions for a field theory where U(1) global symmetry is spontaneously as well as explicitly broken. In the coalesced region of bubble walls, field oscillations result in the decay of the coalesced portion in a large number of defects (e.g. ten vortices and anti-vortices). We discuss the implications of our results for axionic strings in the early Universe, for baryon formation in quark-gluon plasma, and for strings in liquid crystals in the presence of external electric or magnetic field.Production and subsequent evolution of topological defects has been of considerable interest for particle physicists in the context of the early Universe [1]. Similar techniques have also been used to study baryon formation during hadronization of quark-gluon plasma (QGP) in heavy ion collisions [2,3]. Study of topological defects has, of course, been possible in most detailed way only in condensed matter systems where they can be experimentally studied [4].The aforementioned defects correspond to a spontaneous breakdown of a symmetry. However, there are many situations when the symmetry is also explicitly broken. In particle physics, the Pecci-Quinn scheme for solving the strong-CP problem of quantum chromodynamics leads to the presence of an explicit symmetry breaking term and, consequently, to axionic strings [5]. The Skyrmion picture of baryons in the context of chiral models is another example where explicit symmetry breaking terms are needed to incorporate a non-zero pion mass [3]. In condensed matter, liquid crystals provide a simple example of such systems where the presence of external electric or magnetic fields induces explicit symmetry breaking terms [6] The study of formation of topological defects in such systems is therefore important as it has implications for a diverse set of phenomena. It has recently been argued that explicit symmetry breaking can lead to a four fold enhancement in the production of baryons in QGP [3]. These arguments were largely qualitative and did not depend sensitively on the order of the phase transition. It was argued in [3] that a similar enhancement should occur for other topological defects as well.In this letter we demonstrate a new mechanism for the production of topological defects for systems with explicit symmetry breaking and with a first order phase transition, where phase transition proceeds via bubble nucleation. This mechanism leads to a much stronger enhancement in defect production, and results from a combination of the effects discussed in [3] as well as effects coming from the large field oscillations in the region of coalesced bubble walls. The net result is that wall oscillations decay by producing a large number of vortices and antivortices. For example in one simulation, we found 5 vortices and 5 antivortices...

Measuring cosmic defect correlations in liquid crystals

“…In those situations, defect production will be determined by some different processes, e.g. by a new flipping mechanism [17,18], or by fluctuating magnetic fields [19], again, apart from the usual equilibrium thermal production.] Therefore, the expected number of defects per domain has universal behavior, in the sense that it only depends on the symmetry of the order parameter and the space dimensions.…”

Effects of quarks on the formation and evolution of Z(3) walls and strings in an effective model near the QCD deconfining transition

“…Without explicit symmetry breaking, these objects will form via the Kibble mechanism, as discussed in detail in [1]. In the presence of explicit symmetry breaking new effects may arise as discussed in [26] where many string-antistring pairs with small separations (which means small loops of strings or small closed domain walls in the present context) can form at the coalescence region of two bubbles. This mode of production of topological objects arises from the fluctuations of the order parameter and is entirely different from the basic physics of the Kibble mechanism.…”

“…from the different mechanism of production of topological objects as demonstrated in ref. [26]). However, it is still important to see if there are any qualitative differences between the b 1 = 0 case and b 1 = 0 case.…”

Topological String Defect Formation During the Chiral Phase Transition

“…However for the case of explicit symmetry breaking other mechanisms can also contribute to the formation of these defects. In generic situations formation of topological defects is enhanced in systems with explicit symmetry breaking [11]. However, this enhancement crucially depends on the nature of the dynamics of phase transition.…”