B violation with sphalerons and electroweak strings

We show that the sphaleron energy which identifies with the (instanton) potential barrier for B violation is reduced in the presence (background) of an electroweak Z string. We also show that for strings carrying two or more flux quanta the sphaleron energy can go negative. Such electroweak Z strings can then reduce their energy by accumulating sphaleron bound states. As the strings decay, since they are creatures of the broken CP violating phase, the sphalerons will no longer be bound and will thus complete the instanton process preferentially to yield a baryon asymmetry.