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arXiv · 2503.02548

Investigating (Non)-Integrability and Pulsating String in D3-Brane Background

Rashmi R. Nayak·Kamal L. Panigrahi·Manoranjan Samal·Balbeer Singh
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Abstract

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.

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Rashmi R. Nayak, Kamal L. Panigrahi, Manoranjan Samal, Balbeer Singh. 2025-06-19. Investigating (Non)-Integrability and Pulsating String in D3-Brane Background. https://doi.org/10.1140/epjc%2Fs10052-025-14401-9

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