Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models

• Published in: The journal of high energy physics 2019-02, Vol.2019 (2), Article 190
• Main Authors: Fujimori, Toshiaki, Kamata, Syo, Misumi, Tatsuhiro, Nitta, Muneto, Sakai, Norisuke
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2019)190

A bstract We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂ P N − 1 sigma model on ℝ× S 1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the ℂ P N − 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.