Quantum phase transition and resurgence: Lessons from three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics

Fujimori, Toshiaki; Honda, Masazumi; Kamata, Syo; Misumi, Tatsuhiro; Sakai, Norisuke; Yoda, Takuya

doi:10.1093/ptep/ptab086

Cited by 10 publications

(4 citation statements)

References 147 publications

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“…1 In the last years, many works have successfully applied these ideas to QFT [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] providing a novel perspective on various non-perturbative phenomena such as renormalons, instantons, and quark-hadron duality. Moreover, an intimate relation has emerged between resurgence and phase transitions when the latter are seen as Stokes phenomena [34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

The analytic structure of the fixed charge expansion

Antipin

Bersini

Sannino

et al. 2022

J. High Energ. Phys.

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We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are O(N) and QED3. We show that in d = 3 − ϵ dimensions the contribution to the O(N) fixed charge Q conformal dimensions obtained in the double scaling limit of large charge and vanishing ϵ is non-Borel summable, doubly factorial divergent, and with order $$ \sqrt{Q} $$ Q optimal truncation order. By using resurgence techniques we show that the singularities in the Borel plane are related to worldline instantons that were discovered in the other double scaling limit of large Q and N of ref. [1]. In d = 4 − ϵ dimensions the story changes since in the same large Q and small E regime the next order corrections to the scaling dimensions lead to a convergent series. The resummed series displays a new branch cut singularity which is relevant for the stability of the O(N) large charge sector for negative ϵ. Although the QED3 model shares the same large charge behaviour of the O(N) model, we discover that at leading order in the large number of matter field expansion the large charge scaling dimensions are Borel summable, single factorial divergent, and with order Q optimal truncation order.

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Section: Introductionmentioning

confidence: 99%

The analytic structure of the fixed charge expansion

Antipin

Bersini

Sannino

et al. 2022

J. High Energ. Phys.

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show abstract

“…A further type of divergence is generated by renormalization subtraction terms of a certain set of Feynman diagrams. Such a divergence is called a renormalon [12][13][14][15][16] and can often be explicitly associated with a specific large-N limit of the underlying theory [17][18][19][20][21][22][23][24][25]. In this article we will deal with a specific UV-renormalon, i.e.…”

Section: Renormalons and Resurgencementioning

confidence: 99%

Resonant resurgent asymptotics from quantum field theory

Borinsky,

Broadhurst

2022

Preprint

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We perform an all-order resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in six-dimensional scalar φ 3 theory and is governed by a third-order nonlinear differential equation. We augment the factorially divergent perturbative expansion associated to the renormalon by asymptotic expansions to all instanton orders, in a conjectured and well-tested formula. A distinctive feature of this renormalon singularity is the appearance of logarithmic terms, starting at second-instanton order in the trans-series. To highlight this and to illustrate our methods, we also analyze the trans-series for a closely related second-order nonlinear differential equation that exhibits a similarly resonant structure but lacks logarithmic contributions.

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“…[18] distinguishes itself from previous ones because it is based on renormalons and the resurgence theory. First proposed by Ecalle [19] in a purely mathematical context, it has found fertile ground in QFT [20][21][22][23][24][25][26][27][28][29]. Renormalized perturbation theory controls the finiteness of QFT in the proper regime.…”

Section: Introductionmentioning

confidence: 99%

The QCD Adler Function and the Muon g − 2 Anomaly from Renormalons

Maiezza

Vásquez

2022

Symmetry

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We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon’s anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for the muon’s anomalous magnetic moment and the experimental value obtained by the most recent muon g−2 collaboration. The latter shows that the Adler function’s new representation can also be consistent with recent lattice determinations.

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Quantum phase transition and resurgence: Lessons from three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics

Cited by 10 publications

References 147 publications

The analytic structure of the fixed charge expansion

The analytic structure of the fixed charge expansion

Resonant resurgent asymptotics from quantum field theory

The QCD Adler Function and the Muon g − 2 Anomaly from Renormalons

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