Chern Simons condensate from misaligned axions

Abstract

We obtain the non-equilibrium condensate of the Chern Simons density induced by a misaligned homogeneous coherent axion field in linear response. The Chern-Simons dynamical susceptibility is simply related to the axion self-energy, a result that is valid to leading order in the axion coupling but to all orders in the couplings of the gauge fields to other fields within or beyond the standard model except the axion. The induced Chern-Simons density requires renormalization which is achieved by vacuum subtraction. For ultralight axions of mass $m_a$ coupled to electromagnetic fields with coupling $g$, the renormalized high temperature contribution post-recombination is $\langle \vec{E}\cdot\vec{B}\rangle(t) = -\frac{g\,\pi^2\,T^4}{15} \,\overline{a}(t)+ \frac{g \,m^2_a\,T}{16\,\pi}\,\dot{\overline{a}}(t) $ with $\overline{a}(t)$ the dynamical homogeneous axion condensate. We conjecture that emergent axion-like quasiparticle excitations in condensed matter systems may be harnessed to probe cosmological axions and the Chern-Simons condensate. Furthermore, it is argued that a misaligned axion can also induce a non-abelian Chern-Simons condensate of similar qualitative form, and can also ``seed'' chiral symmetry breaking and induce a neutral pion condensate after the QCD phase transition.