Hamilton-Jacobi Solution to Soliton Paths and Triangular Mass Relation in Two-dimensional Extended Supersymmetric Theory

TL;DR

This paper applies Hamilton-Jacobi methods to analyze soliton solutions in a two-dimensional supersymmetric theory, confirming mass bounds and a triangular mass inequality through classical mechanics techniques.

Contribution

It introduces a Hamilton-Jacobi approach to explicitly solve for soliton paths and verify mass relations in 2D extended supersymmetric models.

Findings

Soliton solutions satisfy the Bogomol'nyi bound.

Triangular mass inequality is automatically satisfied.

Hamilton-Jacobi method effectively solves for classical soliton configurations.

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 M_{ij}<M_{ik}+M_{kj} is automatically satisfied.