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Two-loop corrections to large order behavior of φ4 theory

We consider the large order behavior of the perturbative expansion of the scalar φ4 field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additiona...

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Bibliographic Details
Published in:Nuclear physics. B 2017-09, Vol.922 (C), p.293-318
Main Authors: Malatesta, Enrico M., Parisi, Giorgio, Rizzo, Tommaso
Format: Article
Language:English
Online Access:Get full text
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Summary:We consider the large order behavior of the perturbative expansion of the scalar φ4 field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additional Feynman diagram with respect to the previously known one dimensional case, but a careful treatment of renormalization is needed. The propagator and Feynman diagrams were expressed in a form suitable for numerical evaluation. We then obtained explicit expressions summing over O(103) distinct eigenvalues determined numerically with the corresponding eigenfunctions.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2017.07.011