Intercommutation of Semilocal Strings and Skyrmions

Abstract

We study the intercommuting of semilocal strings and Skyrmions, for a wide range of internal parameters, velocities and intersection angles by numerically evolving the equations of motion. We find that the collisions of strings and strings, strings and Skyrmions, and Skyrmions and Skyrmions, all lead to intercommuting for a wide range of parameters. Even the collisions of unstable Skyrmions and strings leads to intercommuting, demonstrating that the phenomenon of intercommuting is very robust, extending to dissimilar field configurations that are not stationary solutions. Even more remarkably, at least for the semilocal U (2) formulation considered here, all intercommutations trigger a reversion to U(1) Nielsen-Olesen strings.Physical systems can have a large number of spontaneously broken symmetries, some of which may be local (gauged) while others may be global. In cases where the symmetries are only partially gauged, or gauged with unequal strengths, semilocal strings may be present [1,2,3,4]. If the gauge couplings are widely disparate, the strings may also be stable. Semilocal string solutions exist in the standard electroweak model, but the SU (2) and U (1) gauge couplings are close enough that the solutions are unstable [5,6]. Recently twisted and current-carrying semilocal string solutions have been discovered that may be stable for other values of parameters [7,8]. Semilocal strings arise in supersymmetric QCD if the number of flavors is larger than the order of the symmetry group [9]. In string theory, they can arise as field theoretic realizations of cosmic D-strings [10], in which case they may play a role in cosmology. The formation of semilocal strings in a phase transition has been studied in Refs. [11,12], in a cosmological setting in Refs. [13,14], and in superstring cosmology [15].In the case of topological gauged [16,17,18] and global [19] U (1) strings, numerical evolution of the field theory equations show that colliding strings intercommute (Fig. 1) for almost [20] any scattering angle and velocity. Thus the probability of intercommuting is unity for topological strings. Qualitative arguments [19,21] have been given in an effort to understand intercommutation of topological strings. In the context of string theory cosmic strings and QCD strings, intercommuting probabilities have been calculated in Refs. [23,24] within various approximations.In this paper we study the interactions of semilocal strings, which are topological structures embedded in the solution space of the partially gauged theory, and the related semilocal Skyrmions which are fat and fuzzy objects (still with one "long", i.e. stringlike dimension) on which strings can terminate, much like strings ending on monopoles. (We shall show below (Figs 1, 2) however, that the termination is dynamic, moving along the string.) The scalar field in a Skyrmion can be arbitrarily close to its vacuum expectation value everywhere, in contrast to a string in which the scalar field magnitude vanishes (which is a nonvacuum value) on some curve. ...

Universal Reconnection of Non-Abelian Cosmic Strings

“…Here, via a different logic and explicit computations, we show the concrete dynamics of the inevitable reconnection (note that [7] does not describe dynamics). Furthermore, our results extend the universality to semilocal strings [8] (N C < N F ), which is consistent with recent numerical simulations [9] ( [10]). Stable semilocal strings are realistic and generic in many supersymmetric grand unified theories [2] and cosmologies [3].…”

“…In the case that collision speed exceeds this limitation, one needs incorporation of the massive modes. As in the case of Abelian-Higgs model, numerical simulations [9,10] showed robustness of the reconnection even for high energy collisions. We hope that, in the future observation, this universality may help for distinguishing solitonic strings from cosmic superstrings/D-branes which have lower reconnection probabilities [6,13].…”

“…The center-of-mass parameter is identified with α and we put it zero. Then, we have β = z 2 1 , and the solution of the equation of motion for β is the same as (9), after the time translation. Finally we have (10), therefore we conclude that reconnection occurs, irrespective of the other moduli parameters a and b.…”

Effective nonintercommutation of local cosmic strings at high collision speeds

“…An interesting open question is whether strings carrying zero modes or bound states will also pass through each other at very high collision speeds. In the particular case of semilocal strings and skyrmions in the Bogomolnyi limit it has recently been found [31] that at the location of the first intercommutation the strings revert to Nielsen-Olesen strings, so we expect the result to hold there as well.…”

Cosmic microwave anisotropies from BPS semilocal strings

“…But even though the string can have a very large (infinite) core, the magnetic flux is nevertheless quantized. It is also worth noting that when two semilocal strings of any width collide, they intercommute [47,48,49] and their widths may revert to the minimum width (i.e., the width of an Abelian Higgs string) [48]. As mentioned earlier, the BPS case arises naturally in, for example, D-term inflationary scenarios, In more generic cases, non-BPS cases will arise.…”