An exact solution of domain wall junction is obtained in a four′ 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. *

BPS equations and wall solutions are studied keeping (part of) supersymmetry (SUSY) manifest. Using N = 1 superfields, massive hyperKähler quotient is introduced to obtain massive N = 2 (8 SUSY) nonlinear sigma models in four dimensions with T * CP n target manifold, which yield BPS wall solutions for the n = 1 case. We also describe massive hyper-Kähler quotient of T * CP 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 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-Kähler 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.

Using an exact solution as a concrete example, Nambu-Goldstone modes on the BPS domain wall junction are worked out for N = 1 supersymmetric theories in four dimensions. 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 Nambu-Goldstone modes on domain wall junctions in the bulk flat space in any dimensions. We formulate mode equations and show that fermion and boson with the same mass come in pairs except massless modes which can appear singly, in accordance with unitary representations of (1, 0) supersymmetry.

Bogomol'nyi-Prasad-Sommerfield ͑BPS͒ walls and junctions are studied in Nϭ1 supersymmetric ͑SUSY͒ 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 1 and admits BPS walls and junctions connecting arbitrary points in moduli space. SUSY conditions in nonlinear sigma models are classified either as stationary points of a superpotential or as 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.