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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2021, том 17, 087, 26 стр. (Mi sigma1769)

Эта публикация цитируется в 6 статьях

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

Michael Borinskya, Gerald V. Dunneb, Max Meynigb

a Nikhef Theory Group, Amsterdam 1098 XG, The Netherlands
b Department of Physics, University of Connecticut, Storrs CT 06269-3046, USA

Аннотация: 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.

Ключевые слова: renormalons, resurgence, non-perturbative corrections, quantum field theory, renormalization, Hopf algebra, trans-series.

MSC: 81T15, 81Q15, 34E10

Поступила: 7 апреля 2021 г.; в окончательном варианте 16 сентября 2021 г.; опубликована 23 сентября 2021 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2021.087



Реферативные базы данных:
ArXiv: 2104.00593


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