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Register a new userInteractions of Non-Abelian Global Strings
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Non-Abelian global strings are expected to form during the chiral phase transition. They have orientational zero modes in the internal space, associated with the vector-like symmetry SU(N)_{L+R} broken in the presence of strings. The interaction among two parallel non-Abelian global strings is derived for general relative orientational zero modes, giving a non-Abelian generalization of the Magnus force. It is shown that when the orientations of the strings are the same, the repulsive force reaches the maximum, whereas when the relative orientation becomes the maximum, no force exists between the strings. For the Abelian case we find a finite volume correction to the known result. The marginal instability of the previously known Abelian eta strings is discussed.
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We study the formation of monopoles and strings in a model where SU(3) is spontaneously broken to U(2)=[SU(2)times U(1)]/ZZ_2, and then to U(1). The first symmetry breaking generates monopoles with both SU(2) and U(1) charges since the vacuum manifold is CC P^2. To study the formation of these monopoles, we explicitly describe an algorithm to detect topologically non-trivial mappings on CC P^2. The second symmetry breaking creates ZZ_2 strings linking either monopole-monopole pairs or monopole-antimonopole pairs. When the strings pull the monopoles together they may create stable monopoles of charge 2 or else annihilate. We determine the length distribution of strings and the fraction of monopoles that will survive after the second symmetry breaking. Possible implications for topological defects produced from the spontaneous breaking of even larger symmetry groups, as in Grand Unified models, are discussed.
Contrary to the standard model that does not admit topologically nontrivial solitons, two Higgs doublet models admit topologically stable vortex strings and domain walls. We numerically confirm the existence of a topological $Z$-string confining fractional $Z$-flux inside. We show that topological strings at $sintheta_W = 0$ limit reduce to non-Abelian strings which possess non-Abelian moduli $S^2$ associated with spontaneous breakdown of the $SU(2)$ custodial symmetry. We numerically solve the equations of motion for various parameter choices. It is found that a gauging $U(1)_Y$ always lowers the tension of the $Z$-string while it keeps that of the $W$-string. On the other hand, a deformation of the Higgs potential is either raising or lowering the tensions of the $Z$-string and $W$-string. We numerically obtain an effective potential for the non-Abelian moduli $S^2$ for various parameter deformations under the restriction $tanbeta=1$. It is the first time to show that there exists a certain parameter region where the topological $W$-string can be the most stable topological excitation, contrary to conventional wisdom of electroweak theories. We also obtain numerical solutions of composites of the string and domain walls in a certain condition.
A renormalizable non-Abelian theory of strong interactions of pions, mediated by rho-mesons, is formulated at tree- and at one-loop level in perturbation theory. Hadron masses are generated through spontaneous symmetry breaking using the Higgs mechanism. Quantization and gauge fixing is achieved using the generalized class of $R_xi$ gauges. As an application of this theory, pion-pion scattering lengths are obtained at tree-level in good agreement with data.
We present cosmic microwave background (CMB) power spectra from recent numerical simulations of cosmic strings in the Abelian Higgs model and compare them to CMB power spectra measured by Planck. We obtain revised constraints on the cosmic string tension parameter $Gmu$. For example, in the $Lambda$CDM model with the addition of strings and no primordial tensor perturbations, we find $Gmu < 2.0 times 10^{-7}$ at 95% confidence, about 20% lower than the value obtained from previous simulations, which had 1/64 of the spatial volume. We investigate the source of the difference, showing that the main cause is an improved treatment of the string evolution across the radiation-matter transition. The increased computational volume also makes possible to simulate fully the physical equations of motion, in which the string cores shrink in comoving coordinates. This, and the larger dynamic range, changes the amplitude of the power spectra by only about 10%, demonstrating that field theory simulations of cosmic strings have now reached the required dynamic range for CMB calculations.
In this article we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian which reduces, in the large mass limit while keeping fixed the Fermi velocity, to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a $zeta$-function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum. PACS: 03.65.-w, 81.05.ue, 73.43.-f
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