Mass deformed world-sheet action of semi-local vortices

The mass deformed effective world-sheet theory of semi local vortices was constructed via the field theoretical method. By Euler-Lagrangian equations, the Ansatze for both the gauge field and the adjoint scalar were solved, this ensures that zero modes of vortices are minimal excitations of the system. Up to the $1/g^2$ order, all profiles are solved. The mass deformed effective action was obtained by integrating out the transverse plane of the vortex string. The effective theory interpolates between the local vortex and the lump. Respecting certain normalization conditions, the effective theory shows a Seiberg-like duality, which agrees with the result of the K\"ahler quotient construction.Comment: 22 pages, non figures. Comments are welcome

Gamma-ray polarization induced by cold electrons via Compton processes

The polarization measurement is an important tool to probe the prompt emission mechanism in gamma-ray bursts (GRBs). The synchrotron photons can be scattered by cold electrons in the outflow via Compton scattering processes. The observed polarization depends on both the photon energy and the viewing angle. With the typical bulk Lorentz factor $\Gamma \sim 200$, photons with energy $E>10$ MeV tend to have smaller polarization than photons with energy $E<1$ MeV. At the right viewing angle, i.e. $\theta \sim \Gamma^{-1}$, the polarization achieves its maximal value, and the polarization angle changes $90^{\circ}$ relative to the initial polarization direction. Thus, the synchrotron radiation plus Compton scattering model can naturally explain the $90^{\circ}$ change of the polarization angle in GRB 100826A.Comment: 19 Pages, 5 figures, 1 tabl

Gamma-ray burst polarization via Compton scattering process

Synchrotron radiation and Compton scattering are widely accepted as the most likely emission mechanisms of some astrophysical phenomena, such as gamma-ray bursts (GRBs) and active galactic nuclei (AGNs). The measurement on polarization of photons provides a useful tool to distinguish different emission mechanisms and structures of the emission region. Based on the differential cross section of a polarized photon scattered by an unpolarized electron of any initial momentum, we derive analytical formula of polarization for beamed photons scattered by isotropic electrons with a power law distribution. Numerical calculations are carried out in four special cases: electrons at rest, Thomson limit, head-on collision and monochromatic electrons. It is found that the maximum polarization can be as high as $100\%$ for low energy photons, if the electrons are at rest. Although polarization is highly suppressed due to the isotropic electrons, a maximum value of \sim 10\% \-- 20\% can still be achieved. Compton scattering process can be used to explain the polarization of GRB 041219A and GRB 100826A.Comment: 22 pages, 5 figure

Toda chain from the kink-antikink lattice

In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated kink and antikink. The leading order force is proportional to exponential decay with respect to the distance between the two nearest kinks or antikinks. The second order force have a similar behavior with the larger decay factor, namely $3\over 2$. We make use of these properties to construct the kink lattice. The dynamics of the kink lattice with leading order force can be identified as ordinary nonperiodic Toda lattice. Also the periodic Toda lattice can be obtained when the number of kink lattice is even. The system of kink lattice with force up to the next order corresponds to a new specific deformation of Toda lattice system. There is no well study on this deformation in the integrable literatures.We found that the deformed Toda system are near integrable system, since the integrability are hindered by high order correction terms. Our work provides a effective theory for kink interactions and a new near or quasi integrable model.Comment: 20 pages no figure

Near integrability of kink lattice with higher order interactions

In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential pattern, and coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuation around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order correction terms, the kink lattice can represent one kind of the generic Toda lattice. With only two sites, the kink lattice is classically integrable. If the number of sites of the lattice is larger than two, the kink lattice is not integrable but a near integrable system. We take use of the Flaschka's variables to study the Lax pair of the kink lattice. These Flaschka's variables have interesting algebraic relations and the non-integrability can be manifested. We also discussed the higher Hamiltonians for the deformed open Toda lattice, which has a similar result as the ordinary deformed Toda

Non-Abelian vortices in the emergent U(2) gauge theory of the Hubbard model

By the spin-fermion formula, the Hubbard model on the honeycomb lattice is represented by a U(2) gauge theory in the mean field method, non-Abelian vortex solutions are constructed based on this theory. The quantization condition shows that the magnetic flux quanta are half-integer. There are $2k$ bosonic zero modes for $k$ winding vortices. For the fermions, there are 2 zero energy states (ZESs) corresponding to the single elementary vortex. In the vortex core and on the edge, the system are in the semi-metal phase with a spin gap and in the insulator phase with N\'eel order phase, and can be mapped to the superconductor in class A and CI, respectively.Comment: 4pages, 2table

Constraining the Bulk Lorentz Factor of GRB Outflow in the Magnetic-dominated Jet Model

Recent observations by the Fermi-LAT showed that there are delayed arrivals of GeV photons relative to the onset of MeV photons in some GRBs. In order to avoid a large optical depth, the minimal value of the Lorentz factor has been estimated to be higher than 1000 in some brightest bursts. In this paper, we present a detailed calculation of the time delay between the MeV and GeV photons in the framework of the magnetic-dominated jet model. We find that the time delay strongly depends on the saturated bulk Lorentz factor of the jet. Inspired by this fact, we use this model to calculate the Lorentz factors of the four brightest Fermi bursts. The results indicate that the Lorentz factors are much smaller than that obtained from the "single-zone" scenario. The short GRB 090510 has a minimal Lorentz factor 385, while the three long bursts GRB 080916c, GRB090902b and GRB 090926 have almost the same Lorentz factors, with an average value near 260. Another interesting result is that, for long bursts, GeV photons are emitted after the bulk Lorentz factor saturates. For the short GRB, however, MeV and GeV photons are emitted at the same phase, i.e., either at the expansion phase or at the coast phase.Comment: 18 pages, 2 figure