2025/03/04 by Nayak, Rashmi R., Panigrahi, Kamal L., Samal, Manoranjan +1 · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2503.02548
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 (AdS3 × S2)\varkappa background, deriving dispersion relations for both short and long strings.