Exact WKB in all sectors. Part I. Potentials with degenerate saddles
Abstract We explore the exact-WKB (EWKB) method through the analysis of Airy and Weber types, with an emphasis on the exact quantization of locally harmonic potentials in multiple sectors. The core innovation of our work lies in introducing a novel complexification approach to the energy parameter u...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2025)100 |
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| author | Tatsuhiro Misumi Cihan Pazarbaşı |
| author_facet | Tatsuhiro Misumi Cihan Pazarbaşı |
| author_sort | Tatsuhiro Misumi |
| collection | DOAJ |
| description | Abstract We explore the exact-WKB (EWKB) method through the analysis of Airy and Weber types, with an emphasis on the exact quantization of locally harmonic potentials in multiple sectors. The core innovation of our work lies in introducing a novel complexification approach to the energy parameter u, distinct from the common complexification of the (semi-classical) expansion parameter used in Borel summability. This new technique allows for continuous analytical continuation across different sectors of a potential while maintaining the exact quantization condition, even before median summation. By redefining the A-cycle above the potential barrier top, we ensure the quantization condition remains real and, by use of the Stokes automorphism and the median resummation, show that the resurgence structure is preserved across transitions between sectors. Furthermore, we discuss the Weber-type exact-WKB method, offering exact estimates for quantum actions around all types of saddle points, generalizing previous results. Through the analysis of these quantum actions, we reveal the presence of S-duality, facilitating the exchange between perturbative and non-perturbative behaviors, and we conjecture the mapping of the P-NP relations between dual theories. Our study encompasses periodic and symmetric double-well potentials, demonstrating that the exact-WKB method captures intricate structures in quantum systems in all sectors, including multi-instanton contributions and the resurgence of quantum actions. |
| format | Article |
| id | doaj-art-adaba0786780452db704194209a3cd4c |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-adaba0786780452db704194209a3cd4c2025-08-20T01:49:44ZengSpringerOpenJournal of High Energy Physics1029-84792025-04-012025416210.1007/JHEP04(2025)100Exact WKB in all sectors. Part I. Potentials with degenerate saddlesTatsuhiro Misumi0Cihan Pazarbaşı1Department of Physics, Kindai UniversityOkinawa Institute of Science and TechnologyAbstract We explore the exact-WKB (EWKB) method through the analysis of Airy and Weber types, with an emphasis on the exact quantization of locally harmonic potentials in multiple sectors. The core innovation of our work lies in introducing a novel complexification approach to the energy parameter u, distinct from the common complexification of the (semi-classical) expansion parameter used in Borel summability. This new technique allows for continuous analytical continuation across different sectors of a potential while maintaining the exact quantization condition, even before median summation. By redefining the A-cycle above the potential barrier top, we ensure the quantization condition remains real and, by use of the Stokes automorphism and the median resummation, show that the resurgence structure is preserved across transitions between sectors. Furthermore, we discuss the Weber-type exact-WKB method, offering exact estimates for quantum actions around all types of saddle points, generalizing previous results. Through the analysis of these quantum actions, we reveal the presence of S-duality, facilitating the exchange between perturbative and non-perturbative behaviors, and we conjecture the mapping of the P-NP relations between dual theories. Our study encompasses periodic and symmetric double-well potentials, demonstrating that the exact-WKB method captures intricate structures in quantum systems in all sectors, including multi-instanton contributions and the resurgence of quantum actions.https://doi.org/10.1007/JHEP04(2025)100Nonperturbative EffectsSolitons Monopoles and InstantonsResummationSupersymmetry and Duality |
| spellingShingle | Tatsuhiro Misumi Cihan Pazarbaşı Exact WKB in all sectors. Part I. Potentials with degenerate saddles Journal of High Energy Physics Nonperturbative Effects Solitons Monopoles and Instantons Resummation Supersymmetry and Duality |
| title | Exact WKB in all sectors. Part I. Potentials with degenerate saddles |
| title_full | Exact WKB in all sectors. Part I. Potentials with degenerate saddles |
| title_fullStr | Exact WKB in all sectors. Part I. Potentials with degenerate saddles |
| title_full_unstemmed | Exact WKB in all sectors. Part I. Potentials with degenerate saddles |
| title_short | Exact WKB in all sectors. Part I. Potentials with degenerate saddles |
| title_sort | exact wkb in all sectors part i potentials with degenerate saddles |
| topic | Nonperturbative Effects Solitons Monopoles and Instantons Resummation Supersymmetry and Duality |
| url | https://doi.org/10.1007/JHEP04(2025)100 |
| work_keys_str_mv | AT tatsuhiromisumi exactwkbinallsectorspartipotentialswithdegeneratesaddles AT cihanpazarbası exactwkbinallsectorspartipotentialswithdegeneratesaddles |