Small Winding-Number Expansion: Vortex Solutions at Critical Coupling

We study an axially symmetric solution of a vortex in the Abelian-Higgs model at critical coupling in detail. Here we propose a new idea for a perturbative expansion of a solution, where the winding number of a vortex is naturally extended to be a real number and the solution is expanded with respect to it around its origin. We test this idea on three typical constants contained in the solution and confirm that this expansion works well with the help of the Pad\'e approximation. For instance, we analytically reproduce the value of the scalar charge of the vortex with an error of $O(10^{-6})$. This expansion is also powerful even for large winding numbers.Comment: 38 pages,48 figure

Superconformal Tensor Calculus on an Orbifold in 5D

Superconformal tensor calculus on an orbifold S^1/Z_2 is given in five-dimensional (5D) spacetime. The four-dimensional superconformal Weyl multiplet and various matter multiplets are induced on the boundary planes from the 5D supermultiplets in the bulk. We identify those induced 4D supermultiplets and clarify a general method for coupling the bulk fields to the matter fields on the boundaries in a superconformal invariant manner.Comment: 31 pages, no figures, LaTeX, version to appear in PT

Off-Shell Formulation of Supergravity on Orbifold

An off-shell formulation is given for the ``supersymmetry in singular spaces'' which has recently been developed in an on-shell formalism by Bergshoeff, Kallosh and Van Proeyen using supersymmetry singlet `coupling constant' field and 4-form multiplier field in five-dimensional space-time. We present this formulation for a general supergravity-Yang-Mills-hypermultiplet coupled system compactified on an orbifold $S^1/Z_2$. Relations between the bulk cosmological constant and brane tensions of the boundary planes are discussed.Comment: 23 pages, no figures, LaTeX, PTPTeX styl

Skyrmions from Instantons inside Domain Walls

Some years ago, Atiyah and Manton described a method to construct approximate Skyrmion solutions from Yang-Mills instantons. Here we present a dynamical realization of this construction using domain walls in a five-dimensional gauge theory. The non-abelian gauge symmetry is broken in each vacuum but restored in the core of the domain wall, allowing instantons to nestle inside the wall. We show that the worldvolume dynamics of the wall is given by the Skyrme model, including the four-derivative term, and the instantons appear as Skyrmions.Comment: 11 pages, 1 figure. v1: References added. v2: typos correcte

Walls and vortices in supersymmetric non-abelian gauge theories

We review recent results on the BPS multi-wall solutions in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Total moduli space of the BPS non-Abelian walls is found to be the complex Grassmann manifold SU(N_F)/[SU(N_C)xSU(N_F-N_C)xU(1)]. Exact solutions are obtained with full generic moduli for infinite gauge coupling. A 1/4 BPS equation is also solved, giving vortices together with the non-Abelian walls and monopoles in the Higgs phase attached to the vortices. The full moduli space of the 1/4 BPS solutions is found to be holomorphic maps from a complex plane to the wall moduli space.Comment: 10pages, 2figures, Contribution to the proceedings of ``NathFest'' at PASCOS conference, Northeastern University, Boston, Ma, August 200

Ghostbusters in f(R)f(R) supergravity

$f(R)$ supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains $R^n$ with $n$ greater than two.We remove the ghost in $f(R)$ supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism~\cite{Fujimori:2016udq}. We show that the mechanism removes the ghost supermultiplet but also terms including $R^n$ with $n\geq3$, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.Comment: 24 pages, v2: comments, references, new section added, version published in JHE