Soliton solution of a gravitating chiral-quark soliton model: dynamical fermion and Dirac-sea in general relativity

Abstract: In this paper, we study Einstein-Dirac system based on a Dirac fermion coupled with a nonlinear chiral field on static spherically symmetric spacetime. Gravitational effects on the dynamical mass of fermions are examined. The chiral-quark soliton model (CQSM) originally was a model of hadron inspired by the low-energy regime of large-$N_\textrm{c}$ QCD, realizing localized fermions with the full inclusion of the Dirac-sea, which is derived from a regularized one-fermion loop. We extend the CQSM in spherically symmetric curved spacetime and coupled with the Einstein gravity. We successfully solve the CQSM and the Einstein equation self-consistently, and obtain the spectral flow of the fermion energies and also of the ADM mass. The Dirac-sea dilutes the effect of the energy-momentum tensor, which induces an inactive point for the impact of gravity even when the localizing matter exists. The Dirac-sea effect becomes dominant for larger dynamical mass $M\sim \langle\barψψ\rangle$, leading to the emergence of the negative ADM mass.