https://doi.org/10.1140/epjc/s10052-025-14401-9
Regular Article - Theoretical Physics
Investigating (non)-integrability and pulsating string in D3-brane background
1
Centre for Ocean, River, Atmosphere and Land Sciences, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India
2
Department of Physics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India
3
Rayagada Autonomous College, 765001, Rayagada, India
a
curiosity1729@kgpian.iitkgp.ac.in
Received:
26
April
2025
Accepted:
2
June
2025
Published online:
18
June
2025
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 
background, deriving dispersion relations for both short and long strings.
© The Author(s) 2025
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