Check-Operators and Quantum Spectral Curves
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called check-operators), which act on the moduli space. It is this approach...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148583 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Check-Operators and Quantum Spectral Curves / A. Mironov, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 123 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1485832019-02-19T01:29:10Z Check-Operators and Quantum Spectral Curves Mironov, A. Morozov, A. We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called check-operators), which act on the moduli space. It is this approach that led to constructing the (quantum) spectral curves and what is now nicknamed the EO/AMM topological recursion. We explain how the non-commutative algebra of check-operators is related to the modular kernels and how symplectic (special) geometry emerges from it in the classical (Seiberg-Witten) limit, where the quantum integrable structures turn into the well studied classical integrability. As time goes, these results turn applicable to more and more theories of physical importance, supporting the old idea that many universality classes of low-energy effective theories contain matrix model representatives. 2017 Article Check-Operators and Quantum Spectral Curves / A. Mironov, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 123 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H70; 81R10; 81R12; 81T13 DOI:10.3842/SIGMA.2017.047 http://dspace.nbuv.gov.ua/handle/123456789/148583 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called check-operators), which act on the moduli space. It is this approach that led to constructing the (quantum) spectral curves and what is now nicknamed the EO/AMM topological recursion. We explain how the non-commutative algebra of check-operators is related to the modular kernels and how symplectic (special) geometry emerges from it in the classical (Seiberg-Witten) limit, where the quantum integrable structures turn into the well studied classical integrability. As time goes, these results turn applicable to more and more theories of physical importance, supporting the old idea that many universality classes of low-energy effective theories contain matrix model representatives. |
| format |
Article |
| author |
Mironov, A. Morozov, A. |
| spellingShingle |
Mironov, A. Morozov, A. Check-Operators and Quantum Spectral Curves Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Mironov, A. Morozov, A. |
| author_sort |
Mironov, A. |
| title |
Check-Operators and Quantum Spectral Curves |
| title_short |
Check-Operators and Quantum Spectral Curves |
| title_full |
Check-Operators and Quantum Spectral Curves |
| title_fullStr |
Check-Operators and Quantum Spectral Curves |
| title_full_unstemmed |
Check-Operators and Quantum Spectral Curves |
| title_sort |
check-operators and quantum spectral curves |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148583 |
| citation_txt |
Check-Operators and Quantum Spectral Curves / A. Mironov, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 123 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT mironova checkoperatorsandquantumspectralcurves AT morozova checkoperatorsandquantumspectralcurves |
| first_indexed |
2023-05-20T17:30:52Z |
| last_indexed |
2023-05-20T17:30:52Z |
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1796153470347116544 |