TY - JOUR

T1 - Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models

AU - Fujimori, Toshiaki

AU - Kamata, Syo

AU - Misumi, Tatsuhiro

AU - Nitta, Muneto

AU - Sakai, Norisuke

N1 - Funding Information:
The authors are grateful to the organizers and participants of “RIMS-iTHEMS International Workshop on Resurgence Theory” at RIKEN, Kobe and “Resurgent Asymptotics in Physics and Mathematics” at Kavli Institute for Theoretical Physics for giving them a chance to deepen their ideas. This work is supported by the Ministry of Education, Culture, Sports, Science, and Technology(MEXT)-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006). This work is also supported in part by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) Grant Numbers 18K03627 (T.
Funding Information:
F.), 16K17677 (T. M.), 16H03984 (M. N.) and 18H01217 (N. S., T. F., T. M. and M. N.). The work of M.N. is also supported in part by a Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (KAKENHI Grant No. 15H05855) from MEXT of Japan. The work of S. K. is supported in part by the US Department of Energy Grant No. DE-FG02-03ER41260.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP 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 ℂP 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.

AB - We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP 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 ℂP 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.

KW - Nonperturbative Effects

KW - Renormalization Regularization and Renormalons

KW - Sigma Models

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U2 - 10.1007/JHEP02(2019)190

DO - 10.1007/JHEP02(2019)190

M3 - Article

AN - SCOPUS:85062274094

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 2

M1 - 190

ER -