2016
DOI: 10.1103/physrevd.94.105002
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Nonperturbative contributions from complexified solutions inCPN1models

Abstract: We discuss the non-perturbative contributions from real and complex saddle point solutions in the CP 1 quantum mechanics with fermionic degrees of freedom, using the Lefschetz thimble formalism beyond the gaussian approximation. We find bion solutions, which correspond to (complexified) instanton-antiinstanton configurations stabilized in the presence of the fermonic degrees of freedom. By computing the one-loop determinants in the bion backgrounds, we obtain the leading order contributions from both the real … Show more

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Cited by 61 publications
(71 citation statements)
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“…CP 1 quantum mechanics is a dimensional reduction of the two-dimensional CP 1 sigma model, which shows asymptotic freedom, dimensional transmutation and the existence of instantons akin to four-dimensional QCD. Contributions from these solutions are evaluated based on Lefschetz-thimble integrals and it is shown that the combined contributions vanish for the SUSY case ǫ = 1, in conformity with the exact results of SUSY [25]. On the other hand, for the non-SUSY case ǫ = 1, the result contains the imaginary ambiguity, which is expected to be cancelled by that arising from the Borel resummation of perturbation series.…”
Section: Introductionsupporting
confidence: 52%
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“…CP 1 quantum mechanics is a dimensional reduction of the two-dimensional CP 1 sigma model, which shows asymptotic freedom, dimensional transmutation and the existence of instantons akin to four-dimensional QCD. Contributions from these solutions are evaluated based on Lefschetz-thimble integrals and it is shown that the combined contributions vanish for the SUSY case ǫ = 1, in conformity with the exact results of SUSY [25]. On the other hand, for the non-SUSY case ǫ = 1, the result contains the imaginary ambiguity, which is expected to be cancelled by that arising from the Borel resummation of perturbation series.…”
Section: Introductionsupporting
confidence: 52%
“…A mathematically rigorous foundation of path integral is now envisaged [6][7][8]. Resurgence has been most precisely studied recently in quantum mechanics (QM) to yield relations between nonperturbative and perturbative contributions systematically [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], 2D quantum field theories (QFT) [30][31][32][33][34][35][36][37][38][39][40][41], 4D QFT [42][43][44][45][46][47][48], supersymmetric (SUSY) gauge theories [49][50][51][52][53], the matrix models and topological string theory [54][55]…”
Section: Introductionmentioning
confidence: 99%
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“…Thus we expect that there is no problem in resurgence in this limit. This is the situation studied in e.g., [23,24,31,[65][66][67][68] and also in this paper.…”
Section: D Sigma Modelsmentioning
confidence: 96%
“…This ∆ deformation we introduce is not fully satisfactory as it is not a genuine path integral deformation but rather corresponds to a mismatch between the number of bosons and fermions only after having localized the path integral. It would be interesting to see if a similar result can be obtained from a bona-fide deformation of the original path integral and perhaps understand how it relates to the thimble decomposition discussed in [60].…”
Section: Discussionmentioning
confidence: 99%