Fractional instantons and bions in the principal chiral model on 



ℝ
2

×

S
1


$$ {\mathrm{\mathbb{R}}}^2\times {S}^1 $$
 with twisted boundary conditions

Nitta, Muneto

doi:10.1007/jhep08(2015)063

Cited by 34 publications

(24 citation statements)

References 99 publications

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“…Models emulating this physical set-up also exhibit non-abelian chiral symmetry breaking [77,[85][86][87][88]. For other roles of the bion saddles in diverse theories, see [89][90][91][92].…”

Section: Magnetic and Neutral Bions In Qcd(adj): Confinement And Centmentioning

confidence: 99%

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Dunne

Ünsal

2016

Annu. Rev. Nucl. Part. Sci.

112

170

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We present a broad conceptual introduction to some new ideas in non-perturbative QFT. The large-N orbifold-orientifold equivalence connects a natural large-N limit of QCD to QCD with adjoint fermions. QCD(adj) with periodic boundary conditions and double-trace deformation of Yang-Mills theory satisfy large-N volume independence, a type of orbifold equivalence. Certain QFTs that satisfy volume independence at N = ∞ exhibit adiabatic continuity at finite-N , and also become semi-classically calculable on small R 3 × S 1 . We discuss the role of monopole-instantons, and magnetic and neutral bion saddles in connection to mass gap, and center and chiral symmetry realizations. Neutral bions also provide a weak coupling semiclassical realization of infrared-renormalons. These considerations help motivate the necessity of complexification of path integrals (Picard-Lefschetz theory) in semi-classical analysis, and highlights the importance of hidden topological angles. Finally, we briefly review the resurgence program, which potentially provides a novel non-perturbative continuum definition of QFT. All these ideas are continuously connected.Keywords: large-N orbifold and orientifold equivalence, volume independence, double-trace deformations, adiabatic continuity, semi-classical calculability, magnetic and neutral bions, Picard-Lefschetz theory of path integration, and resurgence arXiv:1601.03414v1 [hep-th]

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Section: Magnetic and Neutral Bions In Qcd(adj): Confinement And Centmentioning

confidence: 99%

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Dunne

Ünsal

2016

Annu. Rev. Nucl. Part. Sci.

112

170

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“…The conjecture states that the Borel singularity corresponding to the bion could become the renormalon singularity at −2S I /β 0 due to renormalization or decompactification. In spite of the recent progress on compactified CP N −1 models with twisted boundary conditions [103][104][105][106][107] and the intensive studies on the resurgence in the 2D models [108][109][110][111][112][113][114][115][116][117][118][119][120][121][122], the conjecture has not yet been verified even in the 2D sigma models.…”

Section: Introductionmentioning

confidence: 99%

Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models

Fujimori

Kamata

Misumi

et al. 2019

J. High Energ. Phys.

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We derive the semiclassical contributions from the real and complex bions in the twodimensional 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 that the non-perturbative contribution vanishes in the supersymmetric case and it has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity in non-supersymmetric cases. This is the first explicit result indicating the relation between the complex bion and the infrared renormalon. * Electronic address: toshiaki.fujimori018(at)

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“…Within quantum mechanics, it will be interesting to study the thimbles that appear in correlated multi-instanton events beyond second order. In quantum field theory, there are applications to the non-BPS multi-instanton and multi-monopole amplitudes discussed in [55][56][57][58][59][60]. where ω ≡ ω real bion , and t 0 ≡ t real bion 0 .…”

Section: Discussionmentioning

confidence: 99%

Critical points at infinity, non-Gaussian saddles, and bions

Behtash

Dunne

Schäfer

et al. 2018

J. High Energ. Phys.

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It has been argued that many non-perturbative phenomena in quantum mechanics (QM) and quantum field theory (QFT) are determined by complex field configurations, and that these contributions should be understood in terms of Picard-Lefschetz theory. In this work we compute the contribution from non-BPS multi-instanton configurations, such as instanton-anti-instanton [IĪ] pairs, and argue that these contributions should be interpreted as exact critical points at infinity. The Lefschetz thimbles associated with such critical points have a specific structure arising from the presence of non-Gaussian, quasi-zero mode (QZM), directions. When fermion degrees of freedom are present, as in supersymmetric theories, the effective bosonic potential can be written as the sum of a classical and a quantum potential. We show that in this case the semi-classical contribution of the critical point at infinity vanishes, but there is a non-trivial contribution that arises from its associated non-Gaussian QZM-thimble. This approach resolves several puzzles in the literature concerning the semi-classical contribution of correlated [IĪ] pairs. It has the surprising consequence that the configurations dominating the expansion of observables, and the critical points defining the Lefschetz thimble decomposition need not be the same, a feature not present in the traditional Picard-Lefschetz approach.

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Fractional instantons and bions in the principal chiral model on ℝ 2 × S 1 $$ {\mathrm{\mathbb{R}}}^2\times {S}^1 $$ with twisted boundary conditions

Cited by 34 publications

References 99 publications

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models

Critical points at infinity, non-Gaussian saddles, and bions

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