Fermions localized on solitons in flat and curved space-time

Fermionic modes localized on solitons are discussed. Using numerical methods, we construct self-consistent solutions of the corresponding system of coupled integral-differential equations and study dependencies of solitons and normalizable fermion bound states on the values of the parameters of the model. In particular, we consider solutions of (1+1)-dimensional scalar models with self-interaction potentials, including the sine-Gordon model and the polynomial phi^4 and phi^6 models, coupled to the Dirac fermions with a backreaction, and show that presence of fermionic modes leads to formation of static multisoliton bound states. We also study effects of backreaction of the fermionic modes localized by the baby Skyrmion in the (2+1)-dimensional Skyrme model. Considering the effects of gravity we study fermions localized on the static spherically symmetric non-Abelian monopole in the Einstein-Dirac-Yang-Mills-Higgs theory and on the self-gravitating Skyrmion and discuss how the corresponding spectral flows depend on the effective gravitational coupling constant.