Boundary Criticality in Correlated Gapless Topological Matters in 2D and 3D

We investigate the boundary critical behavior of correlated gapless topological systems in two and three dimensions. Dirac quantum spin liquids and Weyl semimetals represent two distinct classes of such phases, described respectively by emergent QED₃ and interacting Weyl fermions coupled to long-range Coulomb interactions. Using renormalization-group analyses, we determine the universal boundary scaling at these fixed points. For Dirac quantum spin liquids, the boundary hosts nontrivial power-law exponents arising from gauge-fluctuation–induced anomalous dimensions in QED₃. In contrast, in Weyl and multi-Weyl semimetals, the interplay between gapless bulk fermions and long-range Coulomb forces produces marginal corrections leading to logarithmic boundary scaling. Our results establish a unified framework for the boundary universality class in correlated gapless topological matter.