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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.02548 |
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| _version_ | 1866918063767552000 |
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| author | Nayak, Rashmi R. Panigrahi, Kamal L. Samal, Manoranjan Singh, Balbeer |
| author_facet | Nayak, Rashmi R. Panigrahi, Kamal L. Samal, Manoranjan Singh, Balbeer |
| contents | This work explores the (non)-integrability and chaotic dynamics of classical strings in the background of a D3-brane with a non-commutative parameter, within the framework of the AdS/CFT correspondence. Using the Polyakov action, we derive the equations of motion and constraints for pulsating strings and analyze their stability through perturbation theory. In the high-energy limit, the first-order perturbed equation simplifies to the Pöschl-Teller equation, solvable via associated Legendre or hypergeometric functions, while numerical methods are employed for generic energy values. We demonstrate that the non-commutative parameter enhances chaotic behavior, as evidenced by the Largest Lyapunov Exponent (LLE). Furthermore, we investigate the integrability of geodesic motion and identify two distinct string modes: captured at and escape to infinity. Finally, we study pulsating strings in the deformed $(AdS_{3} \times S^{2})_{\varkappa}$ background, deriving dispersion relations for both short and long strings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Investigating (Non)-Integrability and Pulsating String in D3-Brane Background Nayak, Rashmi R. Panigrahi, Kamal L. Samal, Manoranjan Singh, Balbeer High Energy Physics - Theory This work explores the (non)-integrability and chaotic dynamics of classical strings in the background of a D3-brane with a non-commutative parameter, within the framework of the AdS/CFT correspondence. Using the Polyakov action, we derive the equations of motion and constraints for pulsating strings and analyze their stability through perturbation theory. In the high-energy limit, the first-order perturbed equation simplifies to the Pöschl-Teller equation, solvable via associated Legendre or hypergeometric functions, while numerical methods are employed for generic energy values. We demonstrate that the non-commutative parameter enhances chaotic behavior, as evidenced by the Largest Lyapunov Exponent (LLE). Furthermore, we investigate the integrability of geodesic motion and identify two distinct string modes: captured at and escape to infinity. Finally, we study pulsating strings in the deformed $(AdS_{3} \times S^{2})_{\varkappa}$ background, deriving dispersion relations for both short and long strings. |
| title | Investigating (Non)-Integrability and Pulsating String in D3-Brane Background |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.02548 |