Quantum field theories and critical phenomena on defects

We construct and investigate quantum fields induced on a d-dimensional dissipationless defect by bulk fields propagating in a (d+1)-dimensional space. All interactions are localized on the defect. We derive a unitary noncanonical quantum field theory on the defect, which is analyzed both in the continuum and on the lattice. The universal critical behavior of the underlying system is determined. It turns out that the O(N)-symmetric φ4 theory, induced on the defect by massless bulk fields, belongs to the universality class of particular d-dimensional spin models with long-range interactions. On the other hand, in the presence of bulk mass the critical behavior crossovers to the one of d-dimensional spin models with short-range interactions.