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

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