Novel knotted non-abelian gauge fields

Abstract

In analogy to null electromagnetic fields we define null YM fields. We show that the null non-abelian $SU(N)$ gauge fields admit a set of $2N^2$ conserved "helicities". We derive null YM solutions that carry finite helicities by uplifting the abelian Hopfion solution and their generalizations. Another method that we implement is to deform YM solutions which do not carry helicities into ones that have nontrivial helicities. A nontrivial non-Abelian solution with helicities is found as a wave of infinite energy. We also discuss non-abelian generalizations of the Bateman parameterization for null abelian gauge fields.

33 pages, 1 figure; references added; summary of main points added in Introduction; explanations added and eq. 4.67 modified