# Axion related questions

I have several question regarding axion. Could anyone give me some brief introduction to what is a axion string, axion field and how is this related to fermion zero mode and chiral zero mode?

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Axionic strings are special cosmic strings defined by the condition that if you look at the axion $a(\phi)$ as a function of the cylindrical coordinate around the cosmic string (which I choose to be along the $z$-axis), it winds around the origin, so $$a(\phi) = a_0 \exp(i\phi)$$ There is a nontrivial "monodromy" around the axionic string, we say. At the very center of the string, $a$ (a complex number) continuously goes to zero. So such an object is protected (at least temporarily, in the case of a gauge $U(1)$ symmetry) by a topological "knot" or "twist". Note that $a$ is a complex scalar field and it is charged under a $U(1)$ group which explains its lightness; the lightness is necessary for it to play its standard role in QCD.