• DOI:10.3842/SIGMA.2021.087
• Corpus ID: 232478641

Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: phi3 QFT in 6 Dimensions

@article{Borinsky2021SemiclassicalTF,
  title={Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: phi3 QFT in 6 Dimensions},
  author={Michael Borinsky and Gerald V. Dunne and Max Meynig},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2021}
}

• M. Borinsky, G. Dunne, Max Meynig
• Published 1 April 2021
• Mathematics
• Symmetry, Integrability and Geometry: Methods and Applications

We analyze the asymptotically free massless scalar φ quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent perturbative solutions to the Kreimer–Connes Hopf-algebraic Dyson–Schwinger equations for the anomalous dimension. This scalar conformal field theory is asymptotically free and has a real Lipatov instanton. In the Hopf-algebraic approach we find a trans-series having an intricate Borel singularity structure, with three distinct but resonant non-perturbative terms, each repeated in an infinite series. These expansions are in terms of the renormalized coupling. The resonant structure leads to powers of logarithmic terms at higher levels of the trans-series, analogous to logarithmic terms arising from interactions between instantons and anti-instantons, but arising from a purely perturbative formalism rather than from a semi-classical analysis.