Non-Abelian Statistics Of Axion Strings

We examine an axion string coupled to a Majorana fermion. It is found that there exist a Majorana-Weyl zero mode on the string. Due to the zero mode, the axion strings obey non-abelian statistics. Fermionic zero modes on topological defects often cause non-trivial phenomena in relativistic quantum field theory. Some examples are fermion number fractionalization [1], baryon number violation in the standard model [2], superconductivity on strings [3], monopole catalysis of proton decay [4, 5], and so on. Geometrical relations between shapes of strings and fermion number violation due to zero modes on the strings were investigated in Ref.[6]. In this paper, we will present a novel phenomenon in relativistic quantum filed theory which comes from fermionic zero modes. Fermionic zero modes cause non-abelian statistics of strings in two spatial dimensions. In two spatial dimensions, exotic generalizations of Fermi and Bose statistics are possible. Wave functions in two spatial dimensions are representations of the braid group under interchanges of identical particles. If the wave functions are vectors and the representation is given by non-abelian matrices, the particle is said to obey non-abelian statistics. A particular type of non-abelian statistics is realized by the non-abelian vortices that occur in theories with spontaneously broken non-abelian [email protected]