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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148583 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Check-Operators and Quantum Spectral Curves / A. Mironov, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 123 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862695745046446080 |
|---|---|
| author | Mironov, A. Morozov, A. |
| author_facet | Mironov, A. Morozov, A. |
| citation_txt | Check-Operators and Quantum Spectral Curves / A. Mironov, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 123 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T16:25:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148583 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:25:39Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mironov, A. Morozov, A. 2019-02-18T16:14:30Z 2019-02-18T16:14:30Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148583 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. This work was performed at the Institute for Information Transmission Problems with the
 financial support of the Russian Science Foundation (Grant No.14-50-00150). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Check-Operators and Quantum Spectral Curves Article published earlier |
| spellingShingle | Check-Operators and Quantum Spectral Curves Mironov, A. Morozov, A. |
| title | 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_short | Check-Operators and Quantum Spectral Curves |
| title_sort | check-operators and quantum spectral curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148583 |
| work_keys_str_mv | AT mironova checkoperatorsandquantumspectralcurves AT morozova checkoperatorsandquantumspectralcurves |