Krylov complexity in 2d CFTs with SL(2, ℝ) deformed Hamiltonians
Abstract In this study, we analyze Krylov Complexity in two-dimensional conformal field theories subjected to deformed SL(2, ℝ) Hamiltonians. In the Vacuum state, we find that the K-Complexity exhibits a universal phase structure. The phase structure involves the K-Complexity exhibiting an oscillato...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-02-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2025)035 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823863437537574912 |
|---|---|
| author | Vinay Malvimat Somnath Porey Baishali Roy |
| author_facet | Vinay Malvimat Somnath Porey Baishali Roy |
| author_sort | Vinay Malvimat |
| collection | DOAJ |
| description | Abstract In this study, we analyze Krylov Complexity in two-dimensional conformal field theories subjected to deformed SL(2, ℝ) Hamiltonians. In the Vacuum state, we find that the K-Complexity exhibits a universal phase structure. The phase structure involves the K-Complexity exhibiting an oscillatory behaviour in the non-heating phase, which contrasts with the exponential growth observed in the heating phase, while it displays polynomial growth at the phase boundary. Furthermore, we extend our analysis to compute the K-Complexity of a light operator in excited states, considering both large-c CFT and free field theory. In the free field theory, we find a state-independent phase structure of K-Complexity. However, in the large-c CFT, the behaviour varies, with the K-Complexity once again displaying exponential growth in the heating phase and polynomial growth at the phase boundary. Notably, the precise exponent governing this growth depends on the heaviness of the state under examination. In the non-heating phase, we observe a transition in K-Complexity behaviour from oscillatory to exponential growth, akin to findings in [1], as it represents a special case within the non-heating phase. |
| format | Article |
| id | doaj-art-bf8860fda6c14da8849b0c468f334133 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-bf8860fda6c14da8849b0c468f3341332025-02-09T12:08:44ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025212810.1007/JHEP02(2025)035Krylov complexity in 2d CFTs with SL(2, ℝ) deformed HamiltoniansVinay Malvimat0Somnath Porey1Baishali Roy2Asia Pacific Center for Theoretical PhysicsDepartment of Physics, Ramakrishna Mission Vivekananda Educational and Research InstituteDepartment of Physics, Ramakrishna Mission Vivekananda Educational and Research InstituteAbstract In this study, we analyze Krylov Complexity in two-dimensional conformal field theories subjected to deformed SL(2, ℝ) Hamiltonians. In the Vacuum state, we find that the K-Complexity exhibits a universal phase structure. The phase structure involves the K-Complexity exhibiting an oscillatory behaviour in the non-heating phase, which contrasts with the exponential growth observed in the heating phase, while it displays polynomial growth at the phase boundary. Furthermore, we extend our analysis to compute the K-Complexity of a light operator in excited states, considering both large-c CFT and free field theory. In the free field theory, we find a state-independent phase structure of K-Complexity. However, in the large-c CFT, the behaviour varies, with the K-Complexity once again displaying exponential growth in the heating phase and polynomial growth at the phase boundary. Notably, the precise exponent governing this growth depends on the heaviness of the state under examination. In the non-heating phase, we observe a transition in K-Complexity behaviour from oscillatory to exponential growth, akin to findings in [1], as it represents a special case within the non-heating phase.https://doi.org/10.1007/JHEP02(2025)035AdS-CFT CorrespondenceConformal and W SymmetryConformal Field Models in String TheoryScale and Conformal Symmetries |
| spellingShingle | Vinay Malvimat Somnath Porey Baishali Roy Krylov complexity in 2d CFTs with SL(2, ℝ) deformed Hamiltonians Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Conformal Field Models in String Theory Scale and Conformal Symmetries |
| title | Krylov complexity in 2d CFTs with SL(2, ℝ) deformed Hamiltonians |
| title_full | Krylov complexity in 2d CFTs with SL(2, ℝ) deformed Hamiltonians |
| title_fullStr | Krylov complexity in 2d CFTs with SL(2, ℝ) deformed Hamiltonians |
| title_full_unstemmed | Krylov complexity in 2d CFTs with SL(2, ℝ) deformed Hamiltonians |
| title_short | Krylov complexity in 2d CFTs with SL(2, ℝ) deformed Hamiltonians |
| title_sort | krylov complexity in 2d cfts with sl 2 r deformed hamiltonians |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Conformal Field Models in String Theory Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP02(2025)035 |
| work_keys_str_mv | AT vinaymalvimat krylovcomplexityin2dcftswithsl2rdeformedhamiltonians AT somnathporey krylovcomplexityin2dcftswithsl2rdeformedhamiltonians AT baishaliroy krylovcomplexityin2dcftswithsl2rdeformedhamiltonians |