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Investigating (non)-integrability and pulsating string in D3-brane background.

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Title: Investigating (non)-integrability and pulsating string in D3-brane background.
Authors: Nayak, Rashmi R.1 (AUTHOR) rashmi@coral.iitkgp.ac.in, Panigrahi, Kamal L.2 (AUTHOR) panigrahi@phy.iitkgp.ac.in, Samal, Manoranjan3 (AUTHOR) manoranjan.phys@gmail.com, Singh, Balbeer2 (AUTHOR) curiosity1729@kgpian.iitkgp.ac.in
Source: European Physical Journal C -- Particles & Fields. Jun2025, Vol. 85 Issue 6, p1-14. 14p.
Subjects: Legendre's functions, Geodesic motion, Lyapunov exponents, Perturbation theory, Dispersion relations
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 (A d S 3 × S 2) ϰ background, deriving dispersion relations for both short and long strings. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Investigating (non)-integrability and pulsating string in D3-brane background.
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  Data: <searchLink fieldCode="AR" term="%22Nayak%2C+Rashmi+R%2E%22">Nayak, Rashmi R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rashmi@coral.iitkgp.ac.in</i><br /><searchLink fieldCode="AR" term="%22Panigrahi%2C+Kamal+L%2E%22">Panigrahi, Kamal L.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> panigrahi@phy.iitkgp.ac.in</i><br /><searchLink fieldCode="AR" term="%22Samal%2C+Manoranjan%22">Samal, Manoranjan</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> manoranjan.phys@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Singh%2C+Balbeer%22">Singh, Balbeer</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> curiosity1729@kgpian.iitkgp.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Jun2025, Vol. 85 Issue 6, p1-14. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Legendre's+functions%22">Legendre's functions</searchLink><br /><searchLink fieldCode="DE" term="%22Geodesic+motion%22">Geodesic motion</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+exponents%22">Lyapunov exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Dispersion+relations%22">Dispersion relations</searchLink>
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  Data: 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 (A d S 3 × S 2) ϰ background, deriving dispersion relations for both short and long strings. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1140/epjc/s10052-025-14401-9
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      – Code: eng
        Text: English
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      – SubjectFull: Legendre's functions
        Type: general
      – SubjectFull: Geodesic motion
        Type: general
      – SubjectFull: Lyapunov exponents
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      – SubjectFull: Perturbation theory
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      – SubjectFull: Dispersion relations
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      – TitleFull: Investigating (non)-integrability and pulsating string in D3-brane background.
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            NameFull: Panigrahi, Kamal L.
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            NameFull: Samal, Manoranjan
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            – D: 01
              M: 06
              Text: Jun2025
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              Y: 2025
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