2025/02/06 by Charlie Cresswell-Hogg, Cresswell-Hogg, Charlie, Daniel F. Litim +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Nuclear physics research studies #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2502.04473
openalex publication_date 2025/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours N, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local interaction functionals of fermion bilinears. The structure implies that local potential approximations are exact, exactly solvable, and that field anomalous dimensions vanish. Theories with non-trivial anomalous dimensions may also arise under conditions that are identified. We further demonstrate that higher derivative interactions are inevitably induced by point-like ones, including at large-N. The local potential flows for fermionic theories with the most general U(N) symmetric interactions are provided. For sample theories with scalar, pseudo-scalar, vector, or axial-vector interactions, we identify conformal fixed points, scaling dimensions, conformal manifolds, and quantum-induced shifts in scaling dimensions of higher derivative interactions. We also study fermion mass generation, and subleading modifications due to finite N corrections. Implications for conformal field theories, and applications in condensed matter and particle physics are indicated.