Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $\phi$3 QFT in 6 Dimensions

Borinsky, Michael; Dunne, Gerald V.; Meynig, Max

doi:10.3842/sigma.2021.087

Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $$\phi$$³ QFT in 6 Dimensions

Journal Article · Thu Sep 23 00:00:00 EDT 2021 · Symmetry, Integrability and Geometry: Methods and Applications

DOI:https://doi.org/10.3842/sigma.2021.087· OSTI ID:1851360

Borinsky, Michael ^[1]; Dunne, Gerald V. ^[2]; Meynig, Max ^[2]

Nikhef Theory Group, Amsterdam (Netherlands); Univ. of Connecticut, Storrs, CT (United States)
Univ. of Connecticut, Storrs, CT (United States)

We analyze the asymptotically free massless scalar $$\phi$$³ 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Connecticut, Storrs, CT (United States)

Sponsoring Organization:: NWO Vidi; USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Organization:: Nikhef Theory Group

Grant/Contract Number:: SC0010339

OSTI ID:: 1851360

Journal Information:: Symmetry, Integrability and Geometry: Methods and Applications, Journal Name: Symmetry, Integrability and Geometry: Methods and Applications Vol. 17; ISSN 1815-0659

Publisher:: Institute of Mathematics, National Academy of Sciences UkraineCopyright Statement

Country of Publication:: United States

Language:: English

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Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $$\phi$$3 QFT in 6 Dimensions

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Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $$\phi$$³ QFT in 6 Dimensions