Nonperturbative contributions from complexified solutions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="double-struck">C</mml:mi><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>models

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

doi:10.1103/physrevd.94.105002

Cited by 60 publications

(71 citation statements)

References 58 publications

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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%

“…In the resurgent trans-series for theories with degenerate vacua, one needs to take account of configurations called "bions" consisting of an instanton and an antiinstanton [2,10], which give imaginary ambiguities can-1 quantum mechanical models with fermionic degrees of freedom (incorporated as the parameter ǫ) [21,25]. 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.…”

Section: Introductionmentioning

confidence: 99%

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Exact resurgent trans-series and multibion contributions to all orders

et al. 2017

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The full resurgent trans-series is found exactly in near-supersymmetric CP 1 quantum mechanics. By expanding in powers of the SUSY breaking deformation parameter, we obtain the first and second expansion coefficients of the ground state energy. They are absolutely convergent series of nonperturbative exponentials corresponding to multi-bions with perturbation series on those backgrounds. We obtain all multi-bion exact solutions for finite time interval in the complexified theory. We sum the semi-classical multi-bion contributions that reproduce the exact result supporting the resurgence to all orders. We also discuss the similar resurgence structure in CP N−1 (N > 2) models. This is the first result in the quantum mechanical model where the resurgent trans-series structure is verified to all orders in nonperturbative multi-bion contributions.

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Section: Introductionsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact resurgent trans-series and multibion contributions to all orders

et al. 2017

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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%

From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling

Yamazaki

Yonekura

2017

J. High Energ. Phys.

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We study four-dimensional SU(N ) Yang-Mills theory on R×T 3 = R×S 1 A ×S 1 B × S 1 C , with a twisted boundary condition by a Z N center symmetry imposed on S 1 B ×S 1 C . This setup has no IR zero modes and hence is free from IR divergences which could spoil transseries expansion for physical observables. Moreover, we show that the center symmetry is preserved at weak coupling regime. This is shown by first reducing the theory on T 2 = S A × S B , to connect the model to the two-dimensional CP N −1 -model. Then, we prove that the twisted boundary condition by the center symmetry for the Yang-Mills is reduced to the twisted boundary condition by the Z N global symmetry of CP N −1 . There are N classical vacua, and fractional instantons connecting those N vacua dynamically restore the center symmetry. We also point out the presence of singularities on the Borel plane which depend on the shape of the compactification manifold, and comment on its implications.

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“…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%

The grin of Cheshire cat resurgence from supersymmetric localization

Dorigoni

Glass

2018

SciPost Phys.

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First we compute the S 2 partition function of the supersymmetric N −1 model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the 1 case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instantonanti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from N to r ∈ . Although for generic real r supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer r to recover the undeformed model.

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Nonperturbative contributions from complexified solutions inCPN−1models

Cited by 60 publications

References 58 publications

Exact resurgent trans-series and multibion contributions to all orders

Exact resurgent trans-series and multibion contributions to all orders

From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling

The grin of Cheshire cat resurgence from supersymmetric localization

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