A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution

Abstract

We map the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model in the Borel plane, where the product of functions get mapped to a convolution product. The two-point function can be expressed as a superposition of general powers of the external momentum. The singularities of the anomalous dimension are shown to lie on the real line in the Borel plane and to be linked to the singularities of the Mellin transform of the one-loop graph. This new approach allows us to enlarge the reach of previous studies on the expansions around those singularities. The asymptotic behavior at infinity of the Borel transform of the solution is beyond the reach of analytical methods and we do a preliminary numerical study, aiming to show that it should remain bounded.

arXiv comment21 pages, 2 figures, use Tikz New version includes corrections asked by referee

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Cited by in corpus (10)

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• Alien calculus and a Schwinger--Dyson equation: two-point function with a nonperturbative mass scale
• Non-Wilsonian ultraviolet completion via transseries
• Ward-Schwinger-Dyson equations in ${\varphi }_6^3$ Quantum Field Theory
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Alien Calculus and non perturbative effects in Quantum Field Theory
• Ladders and rainbows in Minimal Subtraction