Masashi Naganuma

Manifest supersymmetry for BPS walls in N=2 nonlinear sigma models

Abstract BPS equations and wall solutions are studied keeping (part of) supersymmetry (SUSY) manifest. Using N =1 superfields, massive hyper-Kahler quotient is introduced to obtain massive N =2 (8 SUSY) nonlinear sigma models in four dimensions with T ∗ C P n target manifold, which yield BPS wall solutions for the n=1 case. We also describe massive hyper-Kahler quotient of T ∗ C P n by using the harmonic superspace formalism which preserves all SUSY manifestly, and BPS equations and wall solutions are obtained in the n=1 case.

BPS Wall in N=2 SUSY Nonlinear Sigma Model with Eguchi-Hanson Manifold

BPS wall solutions are obtained for N = 2 supersymmetric nonlinear sigma model with Eguchi- Hanson target manifold in a manifestly supersymmetric manner. The model is constructed by a massive hyper-Kahler quotient method both in the N = 1 superfield and in the N = 2 superfield (harmonic superspace). We describe the model in simple terms and give relations between various parameterizations which are useful to describe the model and the solution. Some more details can be found in our previous paper (1) (hep-th/0211103). This article is dedicated to Professor Hiroshi Ezawa on the occasion of his seventieth birthday.

An exact solution of BPS domain wall junction

Abstract An exact solution of domain wall junction is obtained in a four-dimensional N =1 supersymmetric U (1)× U (1)′ gauge theory with three pairs of chiral superfields which is motivated by the N =2 SU (2) gauge theory with one flavor perturbed by an adjoint scalar mass. The solution allows us to evaluate various quantities including a new central charge Y k associated with the junction besides Z k which appears already in domain walls. We find that the new central charge Y k gives a negative contribution to the mass of the domain wall junction whereas the central charge Z k gives a dominant positive contribution. One has to be cautious to identify the central charge Y k alone as the mass of the junction.

Bogomol’nyi-Prasad-Sommerfield walls and junctions in supersymmetric nonlinear sigma models

BPS walls and junctions are studied in N = 1 SUSY nonlinear sigma models in four spacetime dimensions. New BPS junction solutions connecting N discrete vacua are found for nonlinear sigma models with several chiral scalar superfields. A nonlinear sigma model with a single chiral scalar superfield is also found which has a moduli space of the topology of S and admits BPS walls and junctions connecting arbitrary points in moduli space. SUSY condition in nonlinear sigma models are classified either as stationary points of superpotential or singularities of the Kähler metric in field space. The total number of SUSY vacua is invariant under holomorphic field redefinitions if we count “runaway vacua” also.

BPS domain walls in models with flat directions

We consider BPS domain walls in four-dimensional N = 1 supersymmetric models with continuous global symmetry. Since the BPS equation is covariant under a global transformation, the solutions of the BPS walls also have global symmetry. The moduli space of the supersymmetric vacua in such models has non-compact flat directions, and complex BPS walls interpolating between two disjoint flat directions can exist. We examine this possibility in two models with global O(2) symmetry and construct the solutions of such BPS walls.

Bogomol’nyi-Prasad-Sommerfield multiwalls in five-dimensional supergravity

Exact BPS solutions of multi-walls are obtained in five-dimensional supergravity. The solutions contain 2n parameters similarly to the moduli space of the corresponding global SUSY models and have a smooth limit of vanishing gravitational coupling. The models are constructed as gravitational deformations of massive T ∗CPn nonlinear sigma models by using the off-shell formulation of supergravity and massive quaternionic quotient method with U(1)×U(1) gauging. We show that the warp factor can have at most single stationary point in this case. We also obtain BPS multi-wall solutions even for models which reduce to generalizations of massive T ∗CPn models with only U(1) isometry in the limit of vanishing gravitational coupling. At particular values of parameters, isometry of the quaternionic manifolds is enhanced. ∗e-mail address: meto@th.phys.titech.ac.jp †e-mail address: fujita@th.phys.titech.ac.jp ‡e-mail address: naganuma@th.phys.titech.ac.jp §e-mail address: nsakai@th.phys.titech.ac.jp

Wall solution with weak gravity limit in five-dimensional supergravity

Abstract In five-dimensional supergravity, an exact solution of BPS wall is found for a gravitational deformation of the massive Eguchi–Hanson nonlinear sigma model. The warp factor decreases for both infinities of the extra dimension. Thin wall limit gives the Randall–Sundrum model without fine-tuning of input parameters. We also obtain wall solutions with warp factors which are flat or increasing in one side, by varying a deformation parameter of the potential.

An exact solution of BPS junctions and its properties

We have obtained an exact solution for the BPS domain wall junction for a N=1 supersymmetric theory in four dimensions and studied its properties. The model is a simplified version of the N=2 SU(2) gauge theory with N_f=1 broken to N=1 by the mass of the adjoint chiral superfield. We define mode equations and demonstrate explicitly that fermion and boson with the same mass have to come in pairs except massless modes. We work out explicitly massless Nambu-Goldstone (NG) modes on the BPS domain wall junction. We find that their wave functions extend along the wall to infinity (not localized) and are not normalizable. It is argued that this feature is a generic phenomenon of NG modes on domain wall junctions in the bulk flat space in any dimensions. NG fermions exhibit a chiral structure in accordance with unitary representations of (1, 0) supersymmetry algebra where fermion and boson with the same mass come in pairs except massless modes which can appear singly.