Details
| Original language | English |
|---|---|
| Article number | 137507 |
| Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |
| Volume | 835 |
| Early online date | 17 Oct 2022 |
| Publication status | Published - 10 Dec 2022 |
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−3/2×4.967n. 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, Vol. 835, 137507, 10.12.2022.
Research output: Contribution to journal › Article › Research › peer review
}
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 -