Resurgence, Operator Product Expansion, and Remarks on Renormalons in Supersymmetric Yang-Mills

Abstract

I discuss similarities and differences between the resurgence program in quantum mechanics and the operator product expansion in strongly coupled Yang-Mills theories. In $\mathcal{N}=1$ super-Yang-Mills renormalons possess peculiar features that make them different from renormalons in QCD. Their conventional QCD interpretation does not seem to be applicable in supersymmetric Yang-Mills in a straightforward manner.

arXiv comment31 pages, 13 figures. This is a write-up of my talk at the Conference "Resurgence and Trans-series in Quantum, Gauge and String Theories," June 30 - July 4, 2014, CERN; v2. One reference added

References in corpus (7)

• Renormalons
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Snapshots of Hadrons, or the Story of How the Vacuum Medium Determines the Properties of the Classical Mesons Which Are Produced, Live and Die in the QCD Vacuum
• A note on perturbation series in supersymmetric gauge theories
• Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model

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• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• The Resurgence of the Cusp Anomalous Dimension
• Renormalons in integrable field theories
• Remark on the Dunne-Unsal relation in exact semi-classics
• Testing the Bethe ansatz with large N renormalons
• Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$
• The case for duality violations in the analysis of hadronic $\tau$ decays
• Renormalons beyond the Borel plane
• Towards tests of quark-hadron duality with functional analysis and spectral function data
• Infrared Renormalons in Supersymmetric Theories
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory