Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂ P N − 1 models

Fujimori, Toshiaki (0000 0004 1936 9959, Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa, 223-8521, Japan) ; Kamata, Syo (0000 0001 2173 6074, Department of Physics, North Carolina State University, Raleigh, NC, 27695, U.S.A.) ; Misumi, Tatsuhiro (0000 0004 1936 9959, Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa, 223-8521, Japan) (0000 0001 0725 8504, Department of Mathematical Science, Akita University, Akita, 010-8502, Japan) (0000000094465255, iTHEMS, RIKEN, 2-1 Hirasawa, Wako, Saitama, 351-0198, Japan) ; Nitta, Muneto (0000 0004 1936 9959, Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa, 223-8521, Japan) ; Sakai, Norisuke (0000 0004 1936 9959, Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa, 223-8521, Japan)

28 February 2019

Abstract: 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.


Published in: JHEP 1902 (2019) 190
Published by: Springer/SISSA
DOI: 10.1007/JHEP02(2019)190
arXiv: 1810.03768
License: CC-BY-4.0



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