TY - JOUR

T1 - Supersymmetric large-order perturbation with the Nicolai map

AU - Lechtenfeld, Olaf

N1 - Funding Information: We acknowledge illuminating discussions with Hermann Nicolai.

PY - 2022/12/10

Y1 - 2022/12/10

N2 - 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−3/2×4.967n. Such an asymptotic behaviour 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.

AB - 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−3/2×4.967n. Such an asymptotic behaviour 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.

UR - http://www.scopus.com/inward/record.url?scp=85140097712&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2022.137507

DO - 10.1016/j.physletb.2022.137507

M3 - Article

AN - SCOPUS:85140097712

VL - 835

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

M1 - 137507

ER -