The image of self-intersecting QCD strings in four dimensions

Abstract

We numerically examine the self-dual solutions of self-intersecting strings immersed in four dimension. By fixing a frame of reference we are able to show that self-intersecting open strings admit world sheets topologies that are able to support monopole/anti-monopole structures. Furthermore we identify the topologies that can lead to q– q ̄ production and annihilation and numerically estimate the production rate for different instantons. We find an upper bound on the production rate and use that to estimate the string tension μ. By examining the pullback of γ 5 onto the string world sheet we show that regions of chiral symmetry breaking can exist where the string world sheet self-intersects with itself lending credence to the relationship of self-intersecting strings and instantons. We are also able to show that for torus knots, the intersection number ν=4(p−q) which validates an earlier conjectures. A program written in MAPLE is supplied to exhibit the animations of the torus knots in four dimensions. These animations are located at the website http://www-hep.physics.uiowa.edu/~bacus/research.html “Animation Control Panel”.