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”.