2,651 research outputs found
A higher-order Skyrme model
We propose a higher-order Skyrme model with derivative terms of eighth, tenth
and twelfth order. Our construction yields simple and easy-to-interpret
higher-order Lagrangians. We first show that a Skyrmion with higher-order terms
proposed by Marleau has an instability in the form of a baby-Skyrmion string,
while the static energies of our construction are positive definite, implying
stability against time-independent perturbations. However, we also find that
the Hamiltonians of our construction possess two kinds of dynamical
instabilities, which may indicate the instability with respect to
time-dependent perturbations. Different from the well-known Ostrogradsky
instability, the instabilities that we find are intrinsically of nonlinear
nature and also due to the fact that even powers of the inverse metric gives a
ghost-like higher-order kinetic-like term. The vacuum state is, however,
stable. Finally, we show that at sufficiently low energies, our Hamiltonians in
the simplest cases, are stable against time-dependent perturbations.Comment: LaTeX: 42 pages, 3 figures; V2: simplifications implemented in Secs.
5 and 6, and references adde
Knotted domain strings
We construct meta-stable knotted domain strings on the surface of a soliton
of the shape of a torus in 3+1 dimensions. We consider the simplest case of Z2
Wess-Zumino-type domain walls for which we can cover the torus with a domain
string accompanied with an anti-domain string. In this theory, all (p,q)-torus
knots can be realized as a linked pair of a(n) (un)knotted domain string and an
anti-domain string.Comment: 6 pages, 8 figures; V2: extended version with more details about the
host model, the numerics and the stability of the solution
Domain wall Skyrmions
Skyrmions of different dimensions are related by domain walls. We obtain
explicit full numerical solutions of various Skyrmion configurations trapped
inside a domain wall. We find for the quadratic mass-term that multi-Skyrmions
are ring-shaped, and conjecture for the linear mass-term, that the
lowest-energy state of multi-Skyrmions will consist of charge-2 rings
accommodated in a lattice.Comment: LaTeX: 18 pages, 14 figures; V2: typos correcte
Effective field theories on solitons of generic shapes
A class of effective field theories for moduli or collective coordinates on
solitons of generic shapes is constructed. As an illustration, we consider
effective field theories living on solitons in the O(4) non-linear sigma model
with higher-derivative terms.Comment: LaTeX: 6 pages, 1 figure; V2: published version, added discussion of
higher-order correction
Some exact Bradlow vortex solutions
We consider the Bradlow equation for vortices which was recently found by
Manton and find a two-parameter class of analytic solutions in closed form on
nontrivial geometries with non-constant curvature. The general solution to our
class of metrics is given by a hypergeometric function and the area of the
vortex domain by the Gaussian hypergeometric function.Comment: LaTeX: 16 pages, no figures; V2: references added, minor additions;
V3 (published version): toy model added as section 3 and conjecture 1 added
in section 4.
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