Investigating (non)-integrability and pulsating string in D3-brane background - Rashmi R. Nayak; Kamal L. Panigrahi; Manoranjan Samal; Balbeer Singh (European Physical Journal C: Particles and Fields)
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 $$(AdS_{3} × S^{2})_{\varkappa }$$ ( A d S 3 × S 2 ) ϰ background, deriving dispersion relations for both short and long strings.