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Register a new userMonopoles, Strings, and Necklaces in $SO(10)$ and $E_6$
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We employ a variety of symmetry breaking patterns in $SO(10)$ and $E_6$ Grand Unified Theories to demonstrate the appearance of topological defects including magnetic monopoles, strings, and necklaces. We show that independent of the symmetry breaking pattern, a topologically stable superheavy monopole carrying a single unit of Dirac charge as well as color magnetic charge is always present. Lighter intermediate mass topologically stable monopoles carrying two or three quanta of Dirac charge can appear in $SO(10)$ and $E_6$ models respectively. These lighter monopoles as well as topologically stable intermediate scale strings can survive an inflationary epoch. We also show the appearance of a novel necklace configuration in $SO(10)$ broken to the Standard Model via $SU(4)_ctimes SU(2)_Ltimes SU(2)_R$. It consists of $SU(4)_c$ and $SU(2)_R$ monopoles connected by flux tubes. Necklaces consisting of monopoles and antimonopoles joined together by flux tubes are also identified. Even in the absence of topologically stable strings, a monopole-string system can temporarily appear. This system decays by emitting gravity waves and we provide an example in which the spectrum of these waves is strongly peaked around $10^{-4}~{rm Hz}$ with $Omega_{rm gw}h^2simeq 10^{-12}$. This spectrum should be within the detection capability of LISA.
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We consider magnetic monopoles and strings that appear in non-supersymmetric $SO(10)$ and $E_6$ grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter $Gmu$ spans the range $10^{-6}-10^{-30}$, where $G$ is Newtons constant and $mu$ is the string tension. We show how intermediate scale monopoles with mass $sim 10^{13}-10^{14}$ GeV and flux $lesssim 2.8times 10^{-16}$ ${mathrm{cm}^{-2}mathrm{s}^{-1}mathrm{sr}^{-1}}$, and cosmic strings with $Gmu sim 10^{-11}-10^{-10}$ survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio $r$ lies between $0.06$ and $0.003$ depending on the details of the inflationary scenario.
Models of symmetry breaking in the early universe can produce networks of cosmic strings threading t Hooft-Polyakov monopoles. In certain cases there is a larger global symmetry group and the monopoles split into so-called semipoles. These networks are all known as cosmic necklaces. We carry out large-scale field theory simulations of the simplest model containing these objects, confirming that the energy density of networks of cosmic necklaces approaches scaling, i.e. that it remains a constant fraction of the background energy density. The number of monopoles per unit comoving string length is constant, meaning that the density fraction of monopoles decreases with time. Where the necklaces carry semipoles rather than monopoles, we perform the first simulations large enough to demonstrate that they also maintain a constant number per unit comoving string length. We also compare our results to a number of analytical models of cosmic necklaces, finding that none explains our results. We put forward evidence that annihilation of poles on the strings is controlled by a diffusive process, a possibility not considered before. The observational constraints derived in our previous work for necklaces with monopoles can now be safely applied to those with semipoles as well.
In cosmological scenarios based on grand unification, string theory or braneworlds, many kinds of topological or non-topological defects, including monopoles and cosmic strings, are predicted to be formed in the early universe. Here we review specifically the physics of composite objects involving monopoles tied to strings. There is a wide variety of these, including for example dumbbells and necklaces, depending on how many strings attach to each monopole and on the extent to which the various fluxes are confined to the strings. We also briefly survey the prospects for observing such structures, the existing observational limits, and potential evidence for a cosmological role.
Obtaining realistic supersymmetry preserving vacua in the minimal renormalizable supersymmetric $Spin(10)$ GUT model introduces considerations of the non-trivial topology of the vacuum manifold. The $D$-parity of low energy unification schemes gets lifted to a one-parameter subgroup $U(1)_D$ of $Spin(10)$. Yet, the choice of the fields signaling spontaneous symmetry breaking leads to disconnected subsets in the vacuum manifold related by the $D$-parity. The resulting domain walls, existing due to topological reasons but not stable, are identified as topological pseudodefects. We obtain a class of one-parameter paths connecting $D$-parity flipped vacua and compute the energy barrier height along the same. We consider the various patterns of symmetry breaking which can result in either intermediate scale gauge groups or a supersymmetric extension of the Standard Model. If the onset of inflation is subsequent to GUT breaking, as could happen also if inflation is naturally explained by the same GUT, the existence of such pseudodefects can leave signatures in the CMB. Specifically, this could have an impact on the scale invariance of the CMB fluctuations and LSS data at the largest scale.
We embed the flipped SU(5) models into the SO(10) models. After the SO(10) gauge symmetry is broken down to the flipped SU(5) times U(1)_X gauge symmetry, we can split the five/one-plets and ten-plets in the spinor mathbf{16} and mathbf{bar{16}} Higgs fields via the stable sliding singlet mechanism. As in the flipped SU(5) models, these ten-plet Higgs fields can break the flipped SU(5) gauge symmetry down to the Standard Model gauge symmetry. The doublet-triplet splitting problem can be solved naturally by the missing partner mechanism, and the Higgsino-exchange mediated proton decay can be suppressed elegantly. Moreover, we show that there exists one pair of the light Higgs doublets for the electroweak gauge symmetry breaking. Because there exist two pairs of additional vector-like particles with similar intermediate-scale masses, the SU(5) and U(1)_X gauge couplings can be unified at the GUT scale which is reasonably (about one or two orders) higher than the SU(2)_L times SU(3)_C unification scale. Furthermore, we briefly discuss the simplest SO(10) model with flipped SU(5) embedding, and point out that it can not work without fine-tuning.
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