Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations

Borinsky, Michael; Dunne, Gerald V.

doi:10.1016/j.nuclphysb.2020.115096

Title: Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations

Abstract

For certain quantum field theories, the Kreimer-Connes Hopf-algebraic approach to renormalization reduces the Dyson-Schwinger equations to a system of non-linear ordinary differential equations for the expansion coefficients of the renormalized Green's function. We apply resurgent asymptotic analysis to find the trans-series solutions which provide the non-perturbative completion of these formal Dyson-Schwinger expansions. We illustrate the general approach with the concrete example of four dimensional massless Yukawa theory, connecting with the exact functional solution found by Broadhurst and Kreimer. The trans-series solution is associated with the iterative form of the Dyson-Schwinger equations, and displays renormalon-like structure of integer-repeated Borel singularities. Extraction of the Stokes constant is possible due to a property we call ‘functional resurgence’.

Authors:: Borinsky, Michael; Dunne, Gerald V.

Publication Date:: Sat Aug 01 00:00:00 EDT 2020

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

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1635071

Alternate Identifier(s):: OSTI ID: 1657076

Grant/Contract Number:: SC0010339

Resource Type:: Published Article

Journal Name:: Nuclear Physics. B

Additional Journal Information:: Journal Name: Nuclear Physics. B Journal Volume: 957 Journal Issue: C; Journal ID: ISSN 0550-3213

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Borinsky, Michael, and Dunne, Gerald V. Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations.  Netherlands: N. p., 2020. 
Web.  doi:10.1016/j.nuclphysb.2020.115096.

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                    Borinsky, Michael, & Dunne, Gerald V. Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations.  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2020.115096

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                    Borinsky, Michael, and Dunne, Gerald V. Sat .  
"Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations".  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2020.115096.

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@article{osti_1635071,

  title        = {Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations},

  author       = {Borinsky, Michael and Dunne, Gerald V.},

  abstractNote = {For certain quantum field theories, the Kreimer-Connes Hopf-algebraic approach to renormalization reduces the Dyson-Schwinger equations to a system of non-linear ordinary differential equations for the expansion coefficients of the renormalized Green's function. We apply resurgent asymptotic analysis to find the trans-series solutions which provide the non-perturbative completion of these formal Dyson-Schwinger expansions. We illustrate the general approach with the concrete example of four dimensional massless Yukawa theory, connecting with the exact functional solution found by Broadhurst and Kreimer. The trans-series solution is associated with the iterative form of the Dyson-Schwinger equations, and displays renormalon-like structure of integer-repeated Borel singularities. Extraction of the Stokes constant is possible due to a property we call ‘functional resurgence’.},

  doi          = {10.1016/j.nuclphysb.2020.115096},

  journal      = {Nuclear Physics. B},

  number       = C,

  volume       = 957,

  place        = {Netherlands},

  year         = {Sat Aug 01 00:00:00 EDT 2020},

  month        = {Sat Aug 01 00:00:00 EDT 2020}

}

Copy to clipboard

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Title: Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations

Abstract

Citation Formats

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Nonperturbative Ambiguities and the Reality of Resurgent Transseries journal, October 2014

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Renormalization group functions for the Wess–Zumino model: Up to 200 loops through Hopf algebras journal, September 2008

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Renormalons in a general Quantum Field Theory journal, July 2018

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Resurgence of the renormalization group equation journal, April 2020

Improved conformal mapping of the Borel plane journal, February 2001

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An Étude in non-linear Dyson–Schwinger Equations journal, October 2006

A chord diagram expansion coming from some Dyson-Schwinger equations journal, January 2013

Perturbation expansions at large order: results for scalar field theories revisited journal, January 2019

Log expansions from combinatorial Dyson–Schwinger equations journal, April 2020

A primer on resurgent transseries and their asymptotics journal, May 2019

Recursion and Growth Estimates in Renormalizable Quantum Field Theory journal, February 2008

Correlation between pole location and asymptotic behavior for Painlev� I solutions journal, April 1999

Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings journal, February 2003

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Alien calculus and a Schwinger–Dyson equation: two-point function with a nonperturbative mass scale journal, October 2017

Proportions of Irreducible Diagrams journal, September 1970

Dimensional renormalization: Ladders and rainbows journal, October 1996

Generating Asymptotics for Factorially Divergent Sequences journal, October 2018

Lambert-W Solves the Noncommutative $$\varPhi ^4$$-Model journal, October 2019

Minimally subtracted six-loop renormalization of $O (n)$ -symmetric $ϕ^{4}$ theory and critical exponents
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journal, January 2009

Lectures on non-perturbative effects in large N gauge theories, matrix models and strings: Non-perturbative effects in large N gauge theories, matrix models and strings
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Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Padé-Borel resummation
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Exact solutions of Dyson–Schwinger equations for iterated one-loop integrals and propagator-coupling duality
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New Nonperturbative Methods in Quantum Field Theory: From Large- N Orbifold Equivalence to Bions and Resurgence
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Renormalization group functions for the Wess–Zumino model: Up to 200 loops through Hopf algebras
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Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group
journal, January 2001

On a class of linked diagrams II. asymptotics
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Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings
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On a class of linked diagrams, I. Enumeration
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