Borel Summability of Perturbative Series in 4D<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>and 5D<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>Supersymmetric Theories

Honda, Masazumi

doi:10.1103/physrevlett.116.211601

Cited by 36 publications

(63 citation statements)

References 65 publications

(78 reference statements)

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“…This has been discussed in the literature since long ago [7,8]. See e.g., [9][10][11][12][13][14] for various points of view on this issue.…”

Section: Jhep07(2017)088mentioning

confidence: 97%

“…Therefore, all the four moduli parameters of the Yang-Mills 1/N instantons are the translations on R × T 3 . 11 Now the true vacuum structure of the theory at the quantum level is described as follows. First of all, note that in the present case, the 1/N instantons do not have size modulus because all the four moduli are associated to translations on space-time R × T 3 .…”

Section: Jhep07(2017)088mentioning

confidence: 99%

“…This is the crucial difference from the instanton computation on R 4 discussed in the Introduction. 11 For some gauge groups G other than SU(N ), there exist fractional instantons on R × T 3 even without twisting. In those cases, the fact that the four moduli parameters are given by translations on R × T 3 can be seen by using string duality.…”

Section: Jhep07(2017)088mentioning

confidence: 99%

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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 has been discussed in the literature since long ago [7,8]. See e.g., [9][10][11][12][13][14] for various points of view on this issue.…”

Section: Jhep07(2017)088mentioning

confidence: 97%

Section: Jhep07(2017)088mentioning

confidence: 99%

Section: Jhep07(2017)088mentioning

confidence: 99%

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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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“…The first thing we can check from our expansion (48) is that we reproduce the undeformed case (11) or (16) in the case of 1 , i.e. N = 2.…”

Section: Cheshire Cat Resurgencementioning

confidence: 96%

“…In [14,15] the authors considered different supersymmetric theories in 3 and 4 dimensions (see also [16,17]) and analysed in great details the weak coupling expansion of particular observables obtained from supersymmetric localization (see [18] for a pedagogical introduction to localization). Despite supersymmetry the authors showed that the perturbative expansions of the considered observables in 4-d = 2 super Yang-Mills (SYM) were asymptotic but Borel summable, a consequence of the absence of neutral bions configurations as argued in [19,20].…”

Section: Introductionmentioning

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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Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1

Hongo

Misumi

Tanizaki

2019

J. High Energ. Phys.

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We investigate the phase structure of the compactified 2-dimensional nonlinear SU (3)/U (1) 2 flag sigma model with respect to two θ-terms. Based on the circle compactification with the Z 3 -twisted boundary condition, which preserves an 't Hooft anomaly of the original uncompactified theory, we perform the semiclassical analysis based on the dilute instanton gas approximation (DIGA). We clarify classical vacua of the theory and derive fractional instanton solutions connecting these vacua. The resulting phase structure based on DIGA exhibits the quantum phase transitions and triple degeneracy at special points in the (θ 1 , θ 2 )-plane, which is consistent with the phase diagram obtained from the anomaly matching and global inconsistency conditions. This result indicates the adiabatic continuity between the flag sigma models on R 2 and R × S 1 with small compactification radius. We further estimate contributions from instanton-anti-instanton configuration (bion) and show the existence of the imaginary ambiguity, which is expected to be cancelled by that of the perturbative Borel resummation.

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Borel Summability of Perturbative Series in 4DN=2and 5DN=1Supersymmetric Theories

Cited by 36 publications

References 65 publications

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

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

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1

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