On marginal deformations and non-integrability

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Authors

Giataganas, Dimitrios
Zayas, Leopoldo A. Pando
Zoubos, Konstantinos

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Publisher

SpringerOpen Journal

Abstract

We study the interplay between a particular marginal deformation of N = 4 super Yang-Mills theory, the β deformation, and integrability in the holographic setting. Using modern methods of analytic non-integrability of Hamiltonian systems, we find that, when the β parameter takes imaginary values, classical string trajectories on the dual background become non-integrable. We expect the same to be true for generic complex β parameter. By exhibiting the Poincar´e sections and phase space trajectories for the generic complex β case, we provide numerical evidence of strong sensitivity to initial conditions. Our findings agree with expectations from weak coupling that the complex β deformation is non-integrable and provide a rigorous argument beyond the trial and error approach to non-integrability.

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Keywords

AdS-CFT correspondence, Conformal field models in string theory

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Citation

Giataganas D, Zayas LAP & Zoubos K 2014, 'On marginal deformations and non-integrability', Journal of High Energy Physics, vol. 129, no.1, pp.1-16.