Hamilton–jacobi Solution to Soliton Paths and Triangular Mass Relation in Two-Dimensional Extended Supersymmetric Theory

Abstract

D = 2, N = 2 generalized Wess-Zumino theory is investigated by the dimensional reduction from D = 4, N = 1 theory. For each solitonic configuration (i, j) the classical static solution is solved by the Hamilton-Jacobi method of equivalent one-dimensional classical mechanics. It is easily shown that the Bogomol'nyi mass bound is saturated by these solutions and triangular mass inequality

Operator Ordering and Classical Soliton Path in Two-Dimensional N = 2 Supersymmetry With Kähler Potential

“…In this case, K(φ, φ * ) = φ * φ, there is no ordering problem in j µ because ∂ 0 a * and ξ commute. Then we can obtain the correct supersymmtry algebra [4].…”

“…Pursuing this approach, we consider a two-dimensional N = 2 Wess-Zumino type model which consists of n chiral superfields with Kähler potential K(φ, φ * ). When this term is flat, K(φ, φ * ) = φφ * , there was no ordering problem because the target space is flat [4]. We shall admit that general Kähler potential raises the ordering problem.…”

“…with eigenfunction ψ ± (x) = |x| − 3 2 e − 1 4x 2 θ(±x) (4) where θ(x) is a step function. On the other hand +i is not an eigenvalue.…”

“…It also happen in our model in the presence of soliton which saturates the Bogomol'nyi mass bound. In the presence of soliton, there are central extensions in the two-dimensional N = 1 supersymmetry [7] and the two-dimensional N = 2 supersymmetry with a flat metric [4]. We can obtain a central extension in the two-dimensional N = 2 supersymmetry with nonflat Kähler metric in the presence of soliton.…”

Quasisupersymmetric Solitons of Coupled Scalar Fields in Two Dimensions

“…Suppose that this equation has m solutions ϕ (1) , ϕ (2) , · · · , ϕ (m) . When i = j boundary conditions of (i, j)-soliton are…”