Fermion number nonconservation in cold dense fermionic matter in (V-A) gauge theories

It is shown that the ground state of cold neutral fermionic matter in abelian (V-A)-theories at sufficiently high densities is an essentially inhomogeneous state with domains of abnormal matter surrounded by normal vacuum. Inside a domain, the gauge feild condensate is non-zero; its formation makes the number of real fermions to be practically vanishing both inside and outside the domain. In four-dimensional non-abelian (V-A)-theories, the abnormal state of cold neutral fermionic matter is unstable in its turn, and the system transforms back into the normal state with small number of fermions above the topologically non-trivial vacuum. Thus, the fermionic density cannot exceed some critical value in several non-abelian theories