Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}$PN - 1 models

Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke

doi:10.1007/jhep02(2019)190

Bion non-perturbative contributions versus infrared renormalons in two-dimensional $$\mathbb{C}$$P^{N - 1} models

Journal Article · Wed Feb 27 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2019)190· OSTI ID:1609452

Fujimori, Toshiaki ^[1]; Kamata, Syo ^[2]; Misumi, Tatsuhiro ^[3]; Nitta, Muneto ^[4]; Sakai, Norisuke ^[4]

Keio Univ., Kanagawa (Japan); DOE/OSTI
North Carolina State Univ., Raleigh, NC (United States)
Keio Univ., Kanagawa (Japan); Akita Univ. (Japan); Inst. of Physical and Chemical Research (RIKEN), Wako (Japan)
Keio Univ., Kanagawa (Japan)

We derive the semiclassical contributions from the real and complex bions in the two-dimensional $$\mathbb{C}$$P^{N 1} sigma model on $$\mathbb{R}$$×S¹ 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 $$\mathbb{C}$$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.

View Accepted Manuscript (DOE)

Research Organization:: North Carolina State Univ., Raleigh, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-03ER41260

OSTI ID:: 1609452

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation Schiappa, Ricardo; Vaz, Ricardo arXiv https://doi.org/10.48550/arxiv.1302.5138	text	January 2013
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Structure of Lefschetz thimbles in simple fermionic systems Kanazawa, Takuya; Tanizaki, Yuya arXiv https://doi.org/10.48550/arxiv.1412.2802	text	January 2014
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