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We study stabilization of an unstable cosmic string associated with spontaneously broken $U(1)_R$ symmetry, which otherwise causes a dangerous roll-over process. We demonstrate that in a gauge mediation model, messengers can receive enough corrections from the thermal plasma of the supersymmetric standard model particles to stabilize the unstable modes of the string.
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We show that a cosmic string associated with spontaneous $U(1)_R$ symmetry breaking gives a constraint for supersymmetric model building. In some models, the string can be viewed as a tube-like domain wall with a winding number interpolating a false vacuum and a true vacuum. Such string causes inhomogeneous decay of the false vacuum to the true vacuum via rapid expansion of the radius of the tube and hence its formation would be inconsistent with the present Universe. However, we demonstrate that there exist metastable solutions which do not expand rapidly. Furthermore, when the true vacua are degenerate, the structure inside the tube becomes involved. As an example, we show a bamboo-like solution, which suggests a possibility observing an information of true vacua from outside of the tube through the shape and the tension of the tube.
The strategy for assigning $Z_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand unification (GUT) model with three families is used to reduce the number of representations compared to the number in the minimal supersymmetric standard models (MSSMs). The SO(32) heterotic string is used to allow a large nonabelian gauge group SU($N$), $Nge 9$, for the hidden sector such that the number of extra U(1) factors is small. A discrete subgroup of the gauge U(1)s is defined as the $Z_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is achieved by the vacuum expectation values of two index antisymmetric tensor Higgs fields ${bf 10}_{+1}$ and $overline{bf 10}_{-1}$ that led to our word `anti-SU(5). In the illustrated example, the multiplicity 3 in one twisted sector allows the permutation symmetry $S_3$ that leads us to select the third family members and one MSSM pair of the Higgs quintets.
Recently, the chiral superconductivity of the cosmic string in the axion model has gathered attention. The superconductive nature can alter the standard understanding of the cosmology of the axion model. For example, a string loop with a sizable superconducting current can become a stable configuration, which is called a Vorton. The superconductive nature can also affect the cosmological evolution of the string network. In this paper, we study the stability of the superconducting current in the string. We find the superconductivity is indeed stable for a straight string or infinitely small string core size, even if the carrier particles are unstable in the vacuum. However we also find that the carrier particle decays in a curved string in typical axion models, if the carrier particles are unstable in the vacuum. Accordingly, the lifetime of the Vorton is not far from that of the carrier particle in the vacuum.
A surprising result in $e^+ e^-$ collisions is that the particle spectra from the string formed between the expanding quark-antiquark pair have thermal properties even though scatterings appear not to be frequent enough to explain this. We address this problem by considering the finite observable interval of a relativistic quantum string in terms of its reduced density operator by tracing over the complement region. We show how quantum entanglement in the presence of a horizon in spacetime for the causal transfer of information leads locally to a reduced mixed-state density operator. For very early proper time $tau$, we show that the entanglement entropy becomes extensive and scales with the rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature $T_tau=hbar/(2pi k_B tau)$, even in the absence of any scatterings.
We investigate the stability of the pion string in a thermal bath and a dense medium. We find that stability is dependent on the order of the chiral transition. String core stability within the experimentally allowed regime is found only if the chiral transition is second order, and even there the stable region is small, i.e., the temperature below which the core is unstable is close to the critical temperature of the phase transition. We also find that the presence of a dense medium, in addition to the thermal bath, enhances the experimentally accessible region with stable strings. We also argue that once the string core decays, the effective winding of the string persists at large distances from the string core. Our analysis is done both in the chiral limit, which is mainly what has been explored in the literature up to now, and for the physical $h e 0$ case, where a conceptual framework is set up for addressing this regime and some simple estimates are done.
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