Chiral vortices and pseudoscalar condensation due to rotation

We investigate the influence of rotation on the dynamical chiral symmetry breaking in strongly interacting matter. We develop a self-consistent Bogoliubov-de Gennes-like theoretical framework to study the inhomogeneous chiral condensate and the possible chiral vortex state in rotating finite-size matter in four-fermion interacting theories. We show that for sufficiently rapid rotation in $2+1$ dimensions, the ground state can be a chiral vortex state, a type of topological defect in analogy to superfluids and superconductors. The vortex state exhibits pion condensation, providing a new mechanism to realize pseudoscalar condensation in strongly interacting matter.