2025/11/06 by Christoph Kopper, Kopper, Christoph, Pierre Wang +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2511.04509
openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28
We have constructed the mean-field trivial solution of the φ4 theory O(N) model in four dimensions in two previous papers using the flow equations of the renormalization group. Here we establish a relation between the trivial solutions we constructed and perturbation theory. We show that if an UV-cutoff is maintained, we can define a renormalized coupling constant g and obtain the perturbative solutions of the mean-field flow equations at each order in perturbation theory. We prove the local Borel-summability of the renormalized mean-field perturbation theory in the presence of an UV cutoff and show that it is asymptotic to the non-perturbative solution.