Quantum field theory of topological spin dynamics

Topological magnetic materials are promising hosts for novel strongly correlated states. I will present a unifying quantum field theory of a wide range of such materials, which captures their universal and topological dynamics. All topological features arise from the continuum-limit gauge fields that one can calculate starting with a microscopic lattice model. Non-collinear incommensurate magnets are shaped by non-Abelian vector gauge fields, including the Dzyaloshinskii-Moriya interaction. Chiral spin couplings related to topological defects give rise to rank-2 antisymmetric tensor gauge fields. The spin-orbit coupling of mobile electrons is similarly described by non-Abelian gauge fields, including rank-2 tensors related to the 3D Berry flux. All gauge fluxes are generally exchanged between electrons and local moments through Kondo-type interactions. I will discuss applications of this theory to (i) spin-wave dynamics in the presence of Weyl electrons, (ii) instabilities of Weyl semimetals, (iii) fluctuations and temperature-dependence of the anomalous/topological Hall effect, and (iv) topological phase transitions involving monopoles and hedgehogs (which can fractionalize electrons).