Anisotropies in boundary and defect conformal field theories

• Applicant: Dr. Francesco Parisen Toldin
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 576244359

Boundary critical phenomena is experiencing a renewed blossoming, partly driven by advances in condensed matter physics and in conformal field theory. In the presence of boundaries or of defects, renormalization group theory predicts that each universality class controlling the bulk critical behavior potentially splits into different boundary universality classes. One of the central ingredients defining a universality class is the notion of an internal symmetry group. On general grounds, interactions at the boundary may break the bulk symmetry group, leading to a rich interplay between bulk and boundary symmetries in determining the critical behavior. In this research proposal we aim at investigating with Monte Carlo simulations the role of anisotropic interactions, that reduce a symmetry group. Our research proposal develops in two main directions. In the first line of research we propose to study three-dimensional systems in the presence of a surface or of a two-dimensional defect. We consider models where the bulk exhibits a full O(N) symmetry, whereas on the boundary the symmetry is reduced to a subgroup O(M), M < N. In a second line of research we shall study three-dimensional models where interactions reduce the O(N) symmetry group to the cubic group, and consider a symmetry-breaking line defect, where an external field is applied. We will investigate the nature of the residual symmetry group on the line, which may serve as a diagnostic tool to distinguish whether the bulk symmetry is O(N) or the reduced cubic group.

• DFG Programme: Research Grants
• International Connection: United Kingdom
• Cooperation Partner: Dr. Andreas Stergiou