Interacting fixed point for Dirac fermions coupled to dipolar Goldstone modes

Establish that the (2+1)-dimensional critical theory with N flavors of massless Dirac fermions minimally coupled to the spatial pseudo-gauge field formed by dipolar Goldstone modes, including a half-quantized Berry-phase term for the pseudo-gauge field and a longitudinal-mode-dominated coupling, flows to a novel interacting fixed point; characterize its universal properties in the large-N limit.

Background

At the 2-D topological phase transition between mean-field band insulators with different Chern numbers, the continuum description involves massless Dirac fermions strongly coupled to dipolar Goldstone modes acting as a spatial pseudo-gauge field with a half-quantized Berry-phase term. The coupling generates singular self-energies that dominate the bare kinetic terms, suggesting interaction-driven scaling and a dynamical exponent z=3/2.

The authors conjecture that this coupled fermion–Goldstone system defines a new interacting fixed point. While they outline a large-N, self-consistent framework and argue that certain interactions become marginal or irrelevant, a complete, controlled demonstration and characterization of the fixed point (including precise critical exponents and stability) remains to be established.