Quantum Field Theories and Critical Phenomena on Defects

TL;DR

This paper develops a quantum field theory on defects induced by bulk fields in higher dimensions, revealing universal critical behaviors and crossover phenomena between long-range and short-range interactions.

Contribution

It introduces a unitary non-canonical quantum field theory on defects and analyzes its critical behavior in both continuum and lattice settings.

Findings

Induced defect fields exhibit universal critical behavior.

Massless bulk fields lead to long-range interaction universality class.

Bulk mass causes crossover to short-range interaction universality class.

Abstract

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 non-canonical 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 phi^4 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.