Bloch Brane

We investigate a system described by two real scalar fields coupled with gravity in (4, 1) dimensions in warped spacetime involving one extra dimension. The results show that the parameter which controls the way the two scalar fields interact induces the appearence of thick brane which engenders internal structure, driving the energy density to localize inside the brane in a very specific way.Comment: 13 pages, 6 figures; some misprints corrected, to appear in JHE

Modified mode-expansion on a BPS wall related to the nonlinear realization

We propose a modified mode-expansion of the bulk fields in a BPS domain wall background to obtain the effective theory on the wall. The broken SUSY is nonlinearly realized on each mode defined by our mode-expansion. Our work clarifies a relation between two different approaches to derive the effective theory on a BPS wall, {\it i.e.} the nonlinear realization approach and the mode-expansion approach. We also discuss a further modification that respects the Lorentz and $U(1)_R$ symmetries broken by the wall.Comment: LaTeX file, 21 pages, no figure

Bogomol'nyi equations for solitons in Maxwell-Chern-Simons gauge theories with the magnetic moment interaction term

Without assuming rotational invariance, we derive Bogomol'nyi equations for the solitons in the abelian Chern-Simons gauge theories with the anomalous magnetic moment interaction. We also evaluate the number of zero modes around a static soliton configuration.Comment: 9 pages, Revtex, SNUTP-94/6

Gravitating Chern-Simons vortices

The construction of self-dual vortex solutions to the Chern-Simons-Higgs model (with a suitable eighth-order potential) coupled to Einstein gravity in (2 + 1) dimensions is reconsidered. We show that the self-duality condition may be derived from the sole assumption $g_{00} = 1$. Next, we derive a family of exact, doubly self-dual vortex solutions, which interpolate between the symmetrical and asymmetrical vacua. The corresponding spacetimes have two regions at spatial infinity. The eighth-order Higgs potential is positive definite, and closed timelike curves are absent, if the gravitational constant is chosen to be negative.Comment: 11 pages, LaTe

SELF-DUAL ANYONS IN UNIFORM BACKGROUND FIELDS

We study relativistic self-dual Chern-Simons-Higgs systems in the presence of uniform background fields that explicitly break CTP. A rich, but discrete vacuum structure is found when the gauge symmetry is spontaneously broken, while the symmetric phase can have an infinite vacuum degeneracy at tree level. The latter is due to the proliferation of neutral solitonic states that cost zero energy. Various novel self-dual solitons, such as these, are found in both the symmetric and the asymmetric phases. Also by considering a similar system on a two-sphere and the subsequent large sphere limit, we isolate sensible and finite expressions for the conserved angular and linear momenta, which satisfy anomalous commutation relations. We conclude with a few remarks on unresolved issues.Comment: LaTeX, 20 pages, 4 uuencoded figures included

Non-Abelian, Self-Dual Chern-Simons Vortices Coupled to Gravity

In this article we consider $SU(2)$ Chern-Simons/Higgs theory coupled to gravity in three-dimensions. It is shown that for a cylindrically symmetric vortex both the Einstein equations and the field equations can be reduced to a set of first-order Bogomol'nyi equations provided that we choose a specific eighth-order potential.Comment: 21 pages, LATEX, no figure

More on scattering of Chern-Simons vortices

I derive a general formalism for finding kinetic terms of the effective Lagrangian for slowly moving Chern-Simons vortices. Deformations of fields linear in velocities are taken into account. From the equations they must satisfy I extract the kinetic term in the limit of coincident vortices. For vortices passing one over the other there is locally the right-angle scattering. The method is based on analysis of field equations instead of action functional so it may be useful also for nonvariational equations in nonrelativistic models of Condensed Matter Physics.Comment: discussion around Eq.(45) is generalised, one more condition for the local right-angle scattering is adde

FERMION ZERO MODES AND BLACK-HOLE HYPERMULTIPLETS WITH RIGID SUPERSYMMETRY

The gravitini zero modes riding on top of the extreme Reissner-Nordstrom black-hole solution of N=2 supergravity are shown to be normalizable. The gravitini and dilatini zero modes of axion-dilaton extreme black-hole solutions of N=4 supergravity are also given and found to have finite norms. These norms are duality invariant. The finiteness and positivity of the norms in both cases are found to be correlated with the Witten-Israel-Nester construction; however, we have replaced the Witten condition by the pure-spin-3/2 constraint on the gravitini. We compare our calculation of the norms with the calculations which provide the moduli space metric for extreme black holes. The action of the N=2 hypermultiplet with an off-shell central charge describes the solitons of N=2 supergravity. This action, in the Majumdar-Papapetrou multi-black-hole background, is shown to be N=2 rigidly supersymmetric.Comment: 18 pages, LaTe

Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure