Supersymmetric large-order perturbation with the Nicolai map

Abstract

In rigidly supersymmetric quantum theories, the Nicolai map allows one to turn on a coupling constant (from zero to a finite value) by keeping the (free) functional integration measure but subjecting the fields to a particular nonlocal and nonlinear transformation. A recursive perturbative construction of the Nicolai-transformed field configuration expresses it as a power series in the coupling, with its coefficient function at order $n$ being a sum of particular tree diagrams. For a quantum-mechanical example, the size of these tree diagrams (under a certain functional norm) is estimated by the $(n+1)$st power of the field size, and their number grows like $n^{-3/2}\times 4.967^n$. Such an asymptotic behavior translates to a finite convergence radius for the formal perturbative expansion of the Nicolai map, which establishes its non-perturbative existence. The known factorial growth of the number of Feynman diagrams for quantum correlators is reproduced by the combinatorics of free-field Wick contractions as usual. We expect our results to extend to higher dimensions, including super Yang-Mills theory.

1+7 pages, v2: minor corrections, matches published version

References in corpus (6)

• Perturbative linearization of super-Yang-Mills theories in general gauges
• N=4 super Yang-Mills correlators without anti-commuting variables
• Construction method for the Nicolai map in supersymmetric Yang-Mills theories
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Cited by in corpus (1)

• An improved Nicolai map for super Yang-Mills theory