On exact-WKB analysis, resurgent structure, and quantization conditions

Sueishi, Naohisa; Kamata, Syo; Misumi, Tatsuhiro; Ünsal, Mithat

doi:10.1007/jhep12(2020)114

On exact-WKB analysis, resurgent structure, and quantization conditions

Journal Article · Thu Dec 17 00:00:00 EST 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep12(2020)114· OSTI ID:1777086

Sueishi, Naohisa ^[1]; Kamata, Syo ^[2]; Misumi, Tatsuhiro ^[3]; ^[4]

Nagoya Univ. (Japan); North Carolina State University
Jiangxi Normal Univ., Nanchang (China)
Akita Univ., Akita (Japan)
North Carolina State Univ., Raleigh, NC (United States)

There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave functions in the Schrödinger equation. In this work, based on the quantization conditions obtained from the exact-WKB method, we determine the relations between the two formalism and in particular show how the two Stokes phenomena are connected to each other: the Stokes phenomenon leading to the ambiguous contribution of different sectors of the path integral formulation corresponds to the change of the “topology” of the Stoke curves in the exact-WKB analysis. We also clarify the equivalence of different quantization conditions including Bohr-Sommerfeld, path integral and Gutzwiller’s ones. In particular, by reorganizing the exact quantization condition, we improve Gutzwiller’s analysis in a crucial way by bion contributions (incorporating complex periodic paths) and turn it into an exact result. Furthermore, we argue the novel meaning of quasi-moduli integral and provide a relation between the Maslov index and the intersection number of Lefschetz thimbles.

View Accepted Manuscript (DOE)

Research Organization:: North Carolina State Univ., Raleigh, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-03ER41260

OSTI ID:: 1777086

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2020; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (127)

Resurgence of the dressing phase for AdS5 × S5 Arutyunov, Gleb; Dorigoni, Daniele; Savin, Sergei Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/jhep01(2017)055	journal	January 2017
Non-BPS exact solutions and their relation to bions in ℂ P N − 1 models Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/jhep05(2016)057	journal	May 2016
Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio Journal of High Energy Physics, Vol. 2015, Issue 11 https://doi.org/10.1007/jhep11(2015)078	journal	November 2015
Valley instanton versus constrained instanton Aoyama, Hideaki; Harano, Toshiyuki; Sato, Masatoshi Nuclear Physics B, Vol. 466, Issue 1-2 https://doi.org/10.1016/0550-3213(96)00066-1	journal	April 1996
One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings Kuroki, Tsunehide; Sugino, Fumihiko Nuclear Physics B, Vol. 919 https://doi.org/10.1016/j.nuclphysb.2017.03.018	journal	June 2017
Instantons in quantum mechanics: Numerical evidence for a conjecture Zinn‐Justin, J. Journal of Mathematical Physics, Vol. 25, Issue 3 https://doi.org/10.1063/1.526205	journal	March 1984
Exact WKB analysis and cluster algebras Iwaki, Kohei; Nakanishi, Tomoki Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 47 https://doi.org/10.1088/1751-8113/47/47/474009	journal	November 2014
Asymptotics of the Instantons of Painlevé I Garoufalidis, Stavros; Its, Alexander; Kapaev, Andrei International Mathematics Research Notices, Vol. 2012, Issue 3 https://doi.org/10.1093/imrn/rnr029	journal	March 2011
More on the infrared renormalon in SU (N) QCD(adj.) on $\mathbb{R}^3\times S^1$ Ashie, Masahiro; Morikawa, Okuto; Suzuki, Hiroshi Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 9 https://doi.org/10.1093/ptep/ptaa096	journal	August 2020
Resurgence structure to all orders of multi-bions in deformed SUSY quantum mechanics Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro Progress of Theoretical and Experimental Physics, Vol. 2017, Issue 8 https://doi.org/10.1093/ptep/ptx101	journal	August 2017
Three-loop correction to the instanton density. II. The sine-Gordon potential Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V. Physical Review D, Vol. 92, Issue 2 https://doi.org/10.1103/physrevd.92.025047	journal	July 2015
Thimble regularization at work: From toy models to chiral random matrix theories Di Renzo, F.; Eruzzi, G. Physical Review D, Vol. 92, Issue 8 https://doi.org/10.1103/physrevd.92.085030	journal	October 2015
Remark on the Dunne-Ünsal relation in exact semiclassics Gahramanov, Ilmar; Tezgin, Kemal Physical Review D, Vol. 93, Issue 6 https://doi.org/10.1103/physrevd.93.065037	journal	March 2016
More on homological supersymmetric quantum mechanics Behtash, Alireza Physical Review D, Vol. 97, Issue 6 https://doi.org/10.1103/physrevd.97.065002	journal	March 2018
Infrared Renormalons versus Operator Product Expansions in Supersymmetric and Related Gauge Theories Dunne, Gerald V.; Shifman, M.; Ünsal, Mithat Physical Review Letters, Vol. 114, Issue 19 https://doi.org/10.1103/physrevlett.114.191601	journal	May 2015
Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories Sulejmanpasic, Tin Physical Review Letters, Vol. 118, Issue 1 https://doi.org/10.1103/physrevlett.118.011601	journal	January 2017
JWKB Connection-Formula Problem Revisited via Borel Summation Silverstone, Harris J. Physical Review Letters, Vol. 55, Issue 23 https://doi.org/10.1103/physrevlett.55.2523	journal	December 1985
Global asymptotics for multiple integrals with boundaries Howls, C. J.; Delabaere, E. Duke Mathematical Journal, Vol. 112, Issue 2 https://doi.org/10.1215/s0012-9074-02-11221-6	journal	April 2002
The grin of Cheshire cat resurgence from supersymmetric localization Dorigoni, Daniele; Glass, Philip SciPost Physics, Vol. 4, Issue 2 https://doi.org/10.21468/scipostphys.4.2.012	journal	January 2018
On asymptotics and resurgent structures of enumerative Gromov–Witten invariants Couso-Santamaría, Ricardo; Schiappa, Ricardo; Vaz, Ricardo Communications in Number Theory and Physics, Vol. 11, Issue 4 https://doi.org/10.4310/cntp.2017.v11.n4.a1	journal	January 2017
Resurgent functions and splitting problems Sauzin, David arXiv https://doi.org/10.48550/arxiv.0706.0137	text	January 2007
From weak to strong coupling in ABJM theory Drukker, Nadav; Marino, Marcos; Putrov, Pavel arXiv https://doi.org/10.48550/arxiv.1007.3837	text	January 2010
The Resurgence of Instantons in String Theory Aniceto, Inês; Schiappa, Ricardo; Vonk, Marcel arXiv https://doi.org/10.48550/arxiv.1106.5922	preprint	January 2011
Monte Carlo simulations on the Lefschetz thimble: taming the sign problem Cristoforetti, Marco; Di Renzo, Francesco; Mukherjee, Abhishek arXiv https://doi.org/10.48550/arxiv.1303.7204	text	January 2013
Resumming the string perturbation series Grassi, Alba; Marino, Marcos; Zakany, Szabolcs arXiv https://doi.org/10.48550/arxiv.1405.4214	text	January 2014
Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling Tanizaki, Yuya; Koike, Takayuki arXiv https://doi.org/10.48550/arxiv.1406.2386	text	January 2014
Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke arXiv https://doi.org/10.48550/arxiv.1409.3444	text	January 2014
Quantization conditions and functional equations in ABJ(M) theories Grassi, Alba; Hatsuda, Yasuyuki; Marino, Marcos arXiv https://doi.org/10.48550/arxiv.1410.7658	preprint	January 2014
Finite N from Resurgent Large N Couso-Santamaría, Ricardo; Schiappa, Ricardo; Vaz, Ricardo arXiv https://doi.org/10.48550/arxiv.1501.01007	text	January 2015
Three-loop Correction to the Instanton Density. I. The Quartic Double Well Potential Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V. arXiv https://doi.org/10.48550/arxiv.1501.03993	text	January 2015
Hidden topological angles and Lefschetz thimbles Behtash, Alireza; Sulejmanpasic, Tin; Schaefer, Thomas arXiv https://doi.org/10.48550/arxiv.1502.06624	text	January 2015
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral Tanizaki, Yuya; Nishimura, Hiromichi; Kashiwa, Kouji arXiv https://doi.org/10.48550/arxiv.1504.02979	text	January 2015
Resurgence of the Cusp Anomalous Dimension Dorigoni, Daniele; Hatsuda, Yasuyuki arXiv https://doi.org/10.48550/arxiv.1506.03763	text	January 2015
Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke arXiv https://doi.org/10.48550/arxiv.1507.00408	text	January 2015
Lefschetz-thimble analysis of the sign problem in one-site fermion model Tanizaki, Yuya; Hidaka, Yoshimasa; Hayata, Tomoya arXiv https://doi.org/10.48550/arxiv.1509.07146	text	January 2015
Identification of perturbative ambiguity canceled against bion Morikawa, Okuto; Takaura, Hiromasa arXiv https://doi.org/10.48550/arxiv.2003.04759	text	January 2020
Instantons in Quantum Mechanics and Resurgent Expansions Jentschura, Ulrich D.; Zinn-Justin, Jean arXiv https://doi.org/10.48550/arxiv.hep-ph/0405279	text	January 2004
Valley Views: Instantons, Large Order Behaviors, and Supersymmetry Aoyama, Hideaki; Kikuchi, Hisashi; Okouchi, Ikuo arXiv https://doi.org/10.48550/arxiv.hep-th/9808034	text	January 1998
Borel summation of adiabatic invariants Costin, O.; Dupaigne, L.; Kruskal, M. D. arXiv https://doi.org/10.48550/arxiv.math/0608315	preprint	January 2006
Valleys in Quantum Mechanics Aoyama, Hideaki; Kikuchi, Hisashi; Okouchi, Ikuo arXiv https://doi.org/10.48550/arxiv.quant-ph/9710064	text	January 1997
Résurgence de Voros et périodes des courbes hyperelliptiques Dillinger, H.; Delabaere, E.; Pham, Frédéric Annales de l’institut Fourier, Vol. 43, Issue 1 https://doi.org/10.5802/aif.1326	journal	January 1993
Lectures on non-perturbative effects in large N gauge theories, matrix models and strings: Non-perturbative effects in large N gauge theories, matrix models and strings Mariño, M. Fortschritte der Physik, Vol. 62, Issue 5-6 https://doi.org/10.1002/prop.201400005	journal	April 2014
Resurgence of the dressing phase for AdS5 × S5 Arutyunov, Gleb; Dorigoni, Daniele; Savin, Sergei Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)055	journal	January 2017
TBA equations and resurgent Quantum Mechanics Ito, Katsushi; Mariño, Marcos; Shu, Hongfei Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/JHEP01(2019)228	journal	January 2019
Multi-flavor massless QED2 at finite densities via Lefschetz thimbles Tanizaki, Yuya; Tachibana, Motoi Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/JHEP02(2017)081	journal	February 2017
Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)190	journal	February 2019
Structure of Lefschetz thimbles in simple fermionic systems Kanazawa, Takuya; Tanizaki, Yuya Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)044	journal	March 2015
Fractional instantons and bions in the O(N) model with twisted boundary conditions Nitta, Muneto Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)108	journal	March 2015
Resurgent analysis of localizable observables in supersymmetric gauge theories Aniceto, Inês; Russo, Jorge G.; Schiappa, Ricardo Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)172	journal	March 2015
Resumming the string perturbation series Grassi, Alba; Mariño, Marcos; Zakany, Szabolcs Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)038	journal	May 2015
Non-BPS exact solutions and their relation to bions in ℂ P N − 1 models Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)057	journal	May 2016
Exact quantization conditions for the relativistic Toda lattice Hatsuda, Yasuyuki; Mariño, Marcos Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)133	journal	May 2016
The power of perturbation theory Serone, Marco; Spada, Gabriele; Villadoro, Giovanni Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)056	journal	May 2017
Quantum geometry of resurgent perturbative/nonperturbative relations Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)087	journal	May 2017
Microscopic structure of magnetic bions Anber, Mohamed M.; Poppitz, Erich Journal of High Energy Physics, Vol. 2011, Issue 6 https://doi.org/10.1007/JHEP06(2011)136	journal	June 2011
Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)164	journal	June 2014
Adjoint QCD on ℝ3 × S 1 with twisted fermionic boundary conditions Misumi, Tatsuhiro; Kanazawa, Takuya Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)181	journal	June 2014
Critical points at infinity, non-Gaussian saddles, and bions Behtash, Alireza; Dunne, Gerald V.; Schäfer, Thomas Journal of High Energy Physics, Vol. 2018, Issue 6 https://doi.org/10.1007/JHEP06(2018)068	journal	June 2018
Resurgence in η-deformed Principal Chiral Models Demulder, Saskia; Dorigoni, Daniele; Thompson, Daniel C. Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)088	journal	July 2016
Exact WKB analysis of N $$ \mathcal{N} $$ = 2 gauge theories Ashok, Sujay K.; Jatkar, Dileep P.; John, Renjan R. Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)115	journal	July 2016
From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling Yamazaki, Masahito; Yonekura, Kazuya Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)088	journal	July 2017
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects Argyres, Philip C.; Ünsal, Mithat Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)063	journal	August 2012
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 Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)063	journal	August 2015
Pure N = 2 $$ \mathcal{N}=2 $$ super Yang-Mills and exact WKB Kashani-Poor, Amir-Kian; Troost, Jan Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)160	journal	August 2015
Resurgence analysis of 2d Yang-Mills theory on a torus Okuyama, Kazumi; Sakai, Kazuhiro Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/JHEP08(2018)065	journal	August 2018
Lattice ℂPN−1 model with ℤN twisted boundary condition: bions, adiabatic continuity and pseudo-entropy Fujimori, Toshiaki; Itou, Etsuko; Misumi, Tatsuhiro Journal of High Energy Physics, Vol. 2020, Issue 8 https://doi.org/10.1007/JHEP08(2020)011	journal	August 2020
Non-perturbative effects and the refined topological string Hatsuda, Yasuyuki; Mariño, Marcos; Moriyama, Sanefumi Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)168	journal	September 2014
Resurgence of the cusp anomalous dimension Dorigoni, Daniele; Hatsuda, Yasuyuki Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)138	journal	September 2015
Resurgence in sine-Gordon quantum mechanics: exact agreement between multi-instantons and uniform WKB Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)157	journal	September 2015
Resurgence and dynamics of O(N) and Grassmannian sigma models Dunne, Gerald V.; Ünsal, Mithat Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)199	journal	September 2015
Continuity, deconfinement, and (super) Yang-Mills theory Poppitz, Erich; Schäfer, Thomas; Ünsal, Mithat Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)115	journal	October 2012
Resurgence theory, ghost-instantons, and analytic continuation of path integrals Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)041	journal	October 2013
Hybrid Monte Carlo on Lefschetz thimbles — A study of the residual sign problem Fujii, H.; Honda, D.; Kato, M. Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)147	journal	October 2013
Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles Cherman, Aleksey; Dorigoni, Daniele; Ünsal, Mithat Journal of High Energy Physics, Vol. 2015, Issue 10 https://doi.org/10.1007/JHEP10(2015)056	journal	October 2015
Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model Dunne, Gerald V.; Ünsal, Mithat Journal of High Energy Physics, Vol. 2012, Issue 11 https://doi.org/10.1007/JHEP11(2012)170	journal	November 2012
Deconstructing zero: resurgence, supersymmetry and complex saddles Dunne, Gerald V.; Ünsal, Mithat Journal of High Energy Physics, Vol. 2016, Issue 12 https://doi.org/10.1007/JHEP12(2016)002	journal	December 2016
Resurgent Transseries and the Holomorphic Anomaly Couso-Santamaría, Ricardo; Edelstein, José D.; Schiappa, Ricardo Annales Henri Poincaré, Vol. 17, Issue 2 https://doi.org/10.1007/s00023-015-0407-z	journal	March 2015
From Weak to Strong Coupling in ABJM Theory Drukker, Nadav; Mariño, Marcos; Putrov, Pavel Communications in Mathematical Physics, Vol. 306, Issue 2 https://doi.org/10.1007/s00220-011-1253-6	journal	May 2011
The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painlevé II Equation Schiappa, Ricardo; Vaz, Ricardo Communications in Mathematical Physics, Vol. 330, Issue 2 https://doi.org/10.1007/s00220-014-2028-7	journal	April 2014
Nonperturbative Ambiguities and the Reality of Resurgent Transseries Aniceto, Inês; Schiappa, Ricardo Communications in Mathematical Physics, Vol. 335, Issue 1 https://doi.org/10.1007/s00220-014-2165-z	journal	October 2014
Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local $${\mathbb{C}\mathbb{P}^2}$$ C P 2 Couso-Santamaría, Ricardo; Edelstein, José D.; Schiappa, Ricardo Communications in Mathematical Physics, Vol. 338, Issue 1 https://doi.org/10.1007/s00220-015-2358-0	journal	April 2015
Exact WKB and Abelianization for the $$T_3$$ Equation Hollands, Lotte; Neitzke, Andrew Communications in Mathematical Physics, Vol. 380, Issue 1 https://doi.org/10.1007/s00220-020-03875-1	journal	October 2020
Calculation of instanton-anti-instanton contributions in quantum mechanics Bogomolny, E. B. Physics Letters B, Vol. 91, Issue 3-4 https://doi.org/10.1016/0370-2693(80)91014-X	journal	April 1980
Bounce in the valley: study of the extended structures from thick-wall to thin-wall vacuum bubbles Aoyama, Hideaki; Wada, Shinya Physics Letters B, Vol. 349, Issue 3 https://doi.org/10.1016/0370-2693(95)00313-A	journal	April 1995
Multi-instanton contributions in quantum mechanics Zinn-Justin, J. Nuclear Physics B, Vol. 192, Issue 1 https://doi.org/10.1016/0550-3213(81)90197-8	journal	November 1981
A new valley method for instanton deformation Aoyama, Hideaki; Kikuchi, Hisashi Nuclear Physics B, Vol. 369, Issue 1-2 https://doi.org/10.1016/0550-3213(92)90384-N	journal	January 1992
Valley views: instantons, large order behaviors, and supersymmetry Aoyama, Hideaki; Kikuchi, Hisashi; Okouchi, Ikuo Nuclear Physics B, Vol. 553, Issue 3 https://doi.org/10.1016/S0550-3213(99)00263-1	journal	August 1999
Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling Tanizaki, Yuya; Koike, Takayuki Annals of Physics, Vol. 351 https://doi.org/10.1016/j.aop.2014.09.003	journal	December 2014
Aspects of perturbation theory in quantum mechanics: The BenderWu Mathematica ® package Sulejmanpasic, Tin; Ünsal, Mithat Computer Physics Communications, Vol. 228 https://doi.org/10.1016/j.cpc.2017.11.018	journal	July 2018
Identification of perturbative ambiguity canceled against bion Morikawa, Okuto; Takaura, Hiromasa Physics Letters B, Vol. 807 https://doi.org/10.1016/j.physletb.2020.135570	journal	August 2020
Periodic Orbits and Classical Quantization Conditions Gutzwiller, Martin C. Journal of Mathematical Physics, Vol. 12, Issue 3 https://doi.org/10.1063/1.1665596	journal	March 1971
Langer–Cherry derivation of the multi-instanton expansion for the symmetric double well Álvarez, Gabriel Journal of Mathematical Physics, Vol. 45, Issue 8 https://doi.org/10.1063/1.1767988	journal	August 2004
Multi-instantons and multicuts Mariño, Marcos; Schiappa, Ricardo; Weiss, Marlene Journal of Mathematical Physics, Vol. 50, Issue 5 https://doi.org/10.1063/1.3097755	journal	May 2009
Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit Richardson, Jeremy O.; Bauer, Rainer; Thoss, Michael The Journal of Chemical Physics, Vol. 143, Issue 13 https://doi.org/10.1063/1.4932361	journal	October 2015
Uniform asymptotic and JWKB expansions for anharmonic oscillators Álvarez, Gabriel; Casares, Carmen Journal of Physics A: Mathematical and General, Vol. 33, Issue 13 https://doi.org/10.1088/0305-4470/33/13/304	journal	March 2000
Exponentially small corrections in the asymptotic expansion of the eigenvalues of the cubic anharmonic oscillator Álvarez, Gabriel; Casares, Carmen Journal of Physics A: Mathematical and General, Vol. 33, Issue 29 https://doi.org/10.1088/0305-4470/33/29/302	journal	July 2000
Borel summation of adiabatic invariants Costin, O.; Dupaigne, L.; Kruskal, M. D. Nonlinearity, Vol. 17, Issue 4 https://doi.org/10.1088/0951-7715/17/4/019	journal	May 2004
Open string amplitudes and large order behavior in topological string theory Mariño, Marcos Journal of High Energy Physics, Vol. 2008, Issue 03 https://doi.org/10.1088/1126-6708/2008/03/060	journal	March 2008
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings Mariño, Marcos Journal of High Energy Physics, Vol. 2008, Issue 12 https://doi.org/10.1088/1126-6708/2008/12/114	journal	December 2008
Conformality or confinement: (IR)relevance of topological excitations Poppitz, Erich; Ünsal, Mithat Journal of High Energy Physics, Vol. 2009, Issue 09 https://doi.org/10.1088/1126-6708/2009/09/050	journal	September 2009
Quantization conditions and functional equations in ABJ(M) theories Grassi, Alba; Hatsuda, Yasuyuki; Mariño, Marcos Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 11 https://doi.org/10.1088/1751-8113/49/11/115401	journal	February 2016
Convergence from divergence Costin, Ovidiu; Dunne, Gerald V. Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 4 https://doi.org/10.1088/1751-8121/aa9e30	journal	December 2017
A new method to sum divergent power series: educated match Álvarez, Gabriel; Silverstone, Harris J. Journal of Physics Communications, Vol. 1, Issue 2 https://doi.org/10.1088/2399-6528/aa8540	journal	September 2017
Analytic continuation of Chern-Simons theory Witten, Edward Chern-Simons Gauge Theory: 20 Years After https://doi.org/10.1090/amsip/050/19	book	January 2010
Hyperasymptotics for Integrals with Saddles Berry, M. V.; Howls, C. J. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 434, Issue 1892 https://doi.org/10.1098/rspa.1991.0119	journal	September 1991
Hyperasymptotics for multidimensional integrals, exact remainder terms and the global connection problem Howls, C. J. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 453, Issue 1966 https://doi.org/10.1098/rspa.1997.0122	journal	November 1997
Anharmonic Oscillator Bender, Carl M.; Wu, Tai Tsun Physical Review, Vol. 184, Issue 5 https://doi.org/10.1103/PhysRev.184.1231	journal	August 1969
Particle spectrum in model field theories from semiclassical functional integral techniques Dashen, Roger F.; Hasslacher, Brosl; Neveu, André Physical Review D, Vol. 11, Issue 12 https://doi.org/10.1103/PhysRevD.11.3424	journal	June 1975
Monte Carlo simulations on the Lefschetz thimble: Taming the sign problem Cristoforetti, Marco; Di Renzo, Francesco; Mukherjee, Abhishek Physical Review D, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevD.88.051501	journal	September 2013
Uniform WKB, multi-instantons, and resurgent trans-series Dunne, Gerald V.; Ünsal, Mithat Physical Review D, Vol. 89, Issue 10 https://doi.org/10.1103/PhysRevD.89.105009	journal	May 2014
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral Tanizaki, Yuya; Nishimura, Hiromichi; Kashiwa, Kouji Physical Review D, Vol. 91, Issue 10 https://doi.org/10.1103/PhysRevD.91.101701	journal	May 2015
Nonperturbative contributions from complexified solutions in C P N − 1 models Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro Physical Review D, Vol. 94, Issue 10 https://doi.org/10.1103/PhysRevD.94.105002	journal	November 2016
Exact resurgent trans-series and multibion contributions to all orders Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro Physical Review D, Vol. 95, Issue 10 https://doi.org/10.1103/PhysRevD.95.105001	journal	May 2017
Semiclassical Realization of Infrared Renormalons Argyres, Philip; Ünsal, Mithat Physical Review Letters, Vol. 109, Issue 12 https://doi.org/10.1103/PhysRevLett.109.121601	journal	September 2012
Infrared Renormalons versus Operator Product Expansions in Supersymmetric and Related Gauge Theories Dunne, Gerald V.; Shifman, M.; Ünsal, Mithat Physical Review Letters, Vol. 114, Issue 19 https://doi.org/10.1103/PhysRevLett.114.191601	journal	May 2015
Complex Path Integrals and Saddles in Two-Dimensional Gauge Theory Buividovich, P. V.; Dunne, Gerald V.; Valgushev, S. N. Physical Review Letters, Vol. 116, Issue 13 https://doi.org/10.1103/PhysRevLett.116.132001	journal	March 2016
Borel Summability of Perturbative Series in 4D N = 2 and 5D N = 1 Supersymmetric Theories Honda, Masazumi Physical Review Letters, Vol. 116, Issue 21 https://doi.org/10.1103/PhysRevLett.116.211601	journal	May 2016
Discrepancies from Asymptotic Series and Their Relation to Complex Classical Trajectories Balian, R.; Parisi, G.; Voros, A. Physical Review Letters, Vol. 41, Issue 17 https://doi.org/10.1103/PhysRevLett.41.1141	journal	October 1978
JWKB Connection-Formula Problem Revisited via Borel Summation Silverstone, Harris J. Physical Review Letters, Vol. 55, Issue 23 https://doi.org/10.1103/PhysRevLett.55.2523	journal	December 1985
New Nonperturbative Methods in Quantum Field Theory: From Large- N Orbifold Equivalence to Bions and Resurgence Dunne, Gerald V.; Ünsal, Mithat Annual Review of Nuclear and Particle Science, Vol. 66, Issue 1 https://doi.org/10.1146/annurev-nucl-102115-044755	journal	October 2016
Asymptotics and Borel Summability Costin, Ovidiu Chapman and Hall/CRC https://doi.org/10.1201/9781420070323	book	January 2008
Global asymptotics for multiple integrals with boundaries Howls, C. J.; Delabaere, E. Duke Mathematical Journal, Vol. 112, Issue 2 https://doi.org/10.1215/S0012-9074-02-11221-6	journal	April 2002
The grin of Cheshire cat resurgence from supersymmetric localization Dorigoni, Daniele; Glass, Philip SciPost Physics, Vol. 4, Issue 2 https://doi.org/10.21468/SciPostPhys.4.2.012	journal	January 2018
Toward Picard–Lefschetz theory of path integrals, complex saddles and resurgence Behtash, Alireza; Dunne, Gerald V.; Schäfer, Thomas Annals of Mathematical Sciences and Applications, Vol. 2, Issue 1 https://doi.org/10.4310/AMSA.2017.v2.n1.a3	journal	January 2017
Nonperturbative effects and the large-order behavior of matrix models and topological strings Mariño, Marcos; Schiappa, Ricardo; Weiss, Marlene Communications in Number Theory and Physics, Vol. 2, Issue 2 https://doi.org/10.4310/CNTP.2008.v2.n2.a3	journal	January 2008
The resurgence of instantons in string theory Aniceto, Inês; Schiappa, Ricardo; Vonk, Marcel Communications in Number Theory and Physics, Vol. 6, Issue 2 https://doi.org/10.4310/CNTP.2012.v6.n2.a3	journal	January 2012
On asymptotics and resurgent structures of enumerative Gromov–Witten invariants Couso-Santamaría, Ricardo; Schiappa, Ricardo; Vaz, Ricardo Communications in Number Theory and Physics, Vol. 11, Issue 4 https://doi.org/10.4310/CNTP.2017.v11.n4.a1	journal	January 2017

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Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED Fujimori, Toshiaki; Honda, Masazumi; Kamata, Syo arXiv https://doi.org/10.48550/arxiv.2103.13654	text	January 2021

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