Built on

K. Ishikawa, O. Morikawa, A. Nakayama, K. Shibata, H. Suzuki, and H. Takaura, “Infrared renormalon in the supersymmetric ℂ P N − 1 \mathbb{C}P^{N-1} model on ℝ × S 1 \mathbb{R}\times S^{1} ,” arXiv:1908.00373 [hep-th]
Original
1908
Earlier work this paper cites.
M. Ashie, O. Morikawa, H. Suzuki, H. Takaura, and K. Takeuchi, “Infrared renormalon in S U ( N ) SU(N) QCD(adj.) on ℝ 3 × S 1 \mathbb{R}^{3}\times S^{1} ,” arXiv:1909.05489 [hep-th]
Original
1909
Earlier work this paper cites.
E. Brezin, J. C. Le Guillou, and J. Zinn-Justin, “Perturbation Theory at Large Order. 2. Role of the Vacuum Instability,” Phys. Rev
1977
Earlier work this paper cites.
L. N. Lipatov, “Divergence of the Perturbation Theory Series and the Quasiclassical Theory,” Sov. Phys. JETP
1977
Earlier work this paper cites.
A. D’Adda, M. Lüscher, and P. Di Vecchia, “A 1/n Expandable Series of Nonlinear Sigma Models with Instantons,” Nucl. Phys
1978
Earlier work this paper cites.
G. ’t Hooft, “Can We Make Sense Out of Quantum Chromodynamics?,” Subnucl. Ser
1979
Earlier work this paper cites.
E. B. Bogomolny, “CALCULATION OF INSTANTON - ANTI-INSTANTON CONTRIBUTIONS IN QUANTUM MECHANICS,” Phys. Lett
1980
Earlier work this paper cites.
J. Zinn-Justin, “Multi - Instanton Contributions in Quantum Mechanics,” Nucl. Phys
1981
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “Large N N reduction with the Twisted Eguchi-Kawai model,” JHEP
Original
1981
Earlier work this paper cites.
F. David, “Nonperturbative Effects and Infrared Renormalons Within the 1/ N N Expansion of the O( N N ) Nonlinear σ \sigma Model,” Nucl. Phys
1982
Earlier work this paper cites.
T. Eguchi and H. Kawai, “Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory,” Phys. Rev. Lett
1982
Earlier work this paper cites.
D. J. Gross and Y. Kitazawa, “A Quenched Momentum Prescription for Large N Theories,” Nucl. Phys
1982
Earlier work this paper cites.

Similar

F. David, “On the Ambiguity of Composite Operators, IR Renormalons and the Status of the Operator Product Expansion,” Nucl. Phys
1984
Cited alongside, same era.
V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Wilson’s Operator Expansion: Can It Fail?,” Nucl. Phys
1985
Cited alongside, same era.
Cambridge University Press, Cambridge, U.K., 1985
S. Coleman, Aspects of Symmetry · 1985
Cited alongside, same era.
V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Two-Dimensional Sigma Models: Modeling Nonperturbative Effects of Quantum Chromodynamics,” Phys. Rept
1986
Cited alongside, same era.
D. J. Broadhurst and A. L. Kataev, “Connections Between Deep Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond,” Phys. Lett
1993
Cited alongside, same era.

Then

M. Ünsal and L. G. Yaffe, “Large-N volume independence in conformal and confining gauge theories,” JHEP
Original
2010
Later among the works it cites.
M. Lüscher and P. Weisz, “Perturbative analysis of the gradient flow in non-abelian gauge theories,” JHEP
Original
2011
Later among the works it cites.
P. Argyres and M. Ünsal, “A semiclassical realization of infrared renormalons,” Phys. Rev. Lett
Original
2012
Later among the works it cites.
P. C. Argyres and M. Ünsal, “The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects,” JHEP
Original
2012
Later among the works it cites.
G. V. Dunne and M. Ünsal, “Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model,” JHEP

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2019

Renormalon structure in compactified spacetime

Ishikawa, Kosuke, Morikawa, Okuto, Shibata, Kazuya et al.

Understand

We point out that the location of renormalon singularities in theory on a circle-compactified spacetime $\mathbb{R}^{d-1} \times S^1$ (with a small radius $R \Lambda \ll 1$) can differ from that on the non-compactified spacetime $\mathbb{R}^d$.

We argue this under the following assumptions, which are often realized in large $N$ theories with twisted boundary conditions: (i) a loop integrand of a renormalon diagram is volume independent, i.e.
it is not modified by the compactification, and (ii) the loop momentum variable along the $S^1$ direction is not associated with the twisted boundary conditions and takes the values $n/R$ with integer $n$.
We find that the Borel singularity is generally shifted by $-1/2$ in the Borel $u$-plane, where the renormalon ambiguity of $\mathcal{O}(\Lambda^k)$ is changed to $\mathcal{O}(\Lambda^{k-1}/R)$ due to the circle compactification $\mathbb{R}^d \to \mathbb{R}^{d-1} \times S^1$.

Built on

K. Ishikawa, O. Morikawa, A. Nakayama, K. Shibata, H. Suzuki, and H. Takaura, “Infrared renormalon in the supersymmetric ℂ P N − 1 \mathbb{C}P^{N-1} model on ℝ × S 1 \mathbb{R}\times S^{1} ,” arXiv:1908.00373 [hep-th]
Original
1908
Earlier work this paper cites.
M. Ashie, O. Morikawa, H. Suzuki, H. Takaura, and K. Takeuchi, “Infrared renormalon in S U ( N ) SU(N) QCD(adj.) on ℝ 3 × S 1 \mathbb{R}^{3}\times S^{1} ,” arXiv:1909.05489 [hep-th]
Original
1909
Earlier work this paper cites.
E. Brezin, J. C. Le Guillou, and J. Zinn-Justin, “Perturbation Theory at Large Order. 2. Role of the Vacuum Instability,” Phys. Rev
1977
Earlier work this paper cites.
L. N. Lipatov, “Divergence of the Perturbation Theory Series and the Quasiclassical Theory,” Sov. Phys. JETP
1977
Earlier work this paper cites.
A. D’Adda, M. Lüscher, and P. Di Vecchia, “A 1/n Expandable Series of Nonlinear Sigma Models with Instantons,” Nucl. Phys
1978
Earlier work this paper cites.
G. ’t Hooft, “Can We Make Sense Out of Quantum Chromodynamics?,” Subnucl. Ser
1979
Earlier work this paper cites.
E. B. Bogomolny, “CALCULATION OF INSTANTON - ANTI-INSTANTON CONTRIBUTIONS IN QUANTUM MECHANICS,” Phys. Lett
1980
Earlier work this paper cites.
J. Zinn-Justin, “Multi - Instanton Contributions in Quantum Mechanics,” Nucl. Phys
1981
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “Large N N reduction with the Twisted Eguchi-Kawai model,” JHEP
Original
1981
Earlier work this paper cites.
F. David, “Nonperturbative Effects and Infrared Renormalons Within the 1/ N N Expansion of the O( N N ) Nonlinear σ \sigma Model,” Nucl. Phys
1982
Earlier work this paper cites.
T. Eguchi and H. Kawai, “Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory,” Phys. Rev. Lett
1982
Earlier work this paper cites.
D. J. Gross and Y. Kitazawa, “A Quenched Momentum Prescription for Large N Theories,” Nucl. Phys
1982
Earlier work this paper cites.

Similar

F. David, “On the Ambiguity of Composite Operators, IR Renormalons and the Status of the Operator Product Expansion,” Nucl. Phys
1984
Cited alongside, same era.
V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Wilson’s Operator Expansion: Can It Fail?,” Nucl. Phys
1985
Cited alongside, same era.
Cambridge University Press, Cambridge, U.K., 1985
S. Coleman, Aspects of Symmetry · 1985
Cited alongside, same era.
V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Two-Dimensional Sigma Models: Modeling Nonperturbative Effects of Quantum Chromodynamics,” Phys. Rept
1986
Cited alongside, same era.
D. J. Broadhurst and A. L. Kataev, “Connections Between Deep Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond,” Phys. Lett
1993
Cited alongside, same era.

Then

M. Ünsal and L. G. Yaffe, “Large-N volume independence in conformal and confining gauge theories,” JHEP
Original
2010
Later among the works it cites.
M. Lüscher and P. Weisz, “Perturbative analysis of the gradient flow in non-abelian gauge theories,” JHEP
Original
2011
Later among the works it cites.
P. Argyres and M. Ünsal, “A semiclassical realization of infrared renormalons,” Phys. Rev. Lett
Original
2012
Later among the works it cites.
P. C. Argyres and M. Ünsal, “The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects,” JHEP
Original
2012
Later among the works it cites.
G. V. Dunne and M. Ünsal, “Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model,” JHEP

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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P. Ball, M. Beneke, and V. M. Braun, “Resummation of ( β 0 α s ) N (\beta_{0}\alpha_{s})^{N} Corrections in QCD: Techniques and Applications to the Tau Hadronic Width and the Heavy Quark Pole Mass,” Nucl. Phys

1995

Cited alongside, same era.

M. Beneke and V. M. Braun, “Naive Nonabelianization and Resummation of Fermion Bubble Chains,” Phys. Lett

1995

Cited alongside, same era.

M. Beneke, V. M. Braun, and N. Kivel, “The Operator product expansion, nonperturbative couplings and the Landau pole: Lessons from the O(N) sigma model,” Phys. Lett

1998

Cited alongside, same era.

M. Beneke, “Renormalons,” Phys. Rept

1999

Cited alongside, same era.

P. Kovtun, M. Ünsal, and L. G. Yaffe, “Volume independence in large N(c) QCD-like gauge theories,” JHEP

2007

Cited alongside, same era.

M. Ünsal and L. G. Yaffe, “Center-stabilized Yang-Mills theory: Confinement and large N volume independence,” Phys. Rev

Original

2008

Cited alongside, same era.