Semiclassical strings in marginally deformed toric AdS/CFT

Lozano

Picos

et al. 2012

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We analyze the holographic description of non-singlet baryons in various backgrounds with reduced supersymmetries and/or confinement. We show that they exist in all AdS 5 × Y 5 backgrounds with Y 5 an Einstein manifold bearing five form flux, for a number of quarks 5N/8 < k N, independently on the supersymmetries preserved. This result still holds for γ i deformations. In the confining Maldacena-Nuñez background nonsinglet baryons also exist, although in this case the interval for the number of quarks is reduced as compared to the conformal case. We generalize these configurations to include a non-vanishing magnetic flux such that a complementary microscopical description can be given in terms of lower dimensional branes expanding into fuzzy baryons. This description is a first step towards exploring the finite 't Hooft coupling region.

Section: Discussionmentioning

confidence: 68%

Non-singlet baryons in less supersymmetric backgrounds

Lozano

Picos

et al. 2012

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“…It would be interesting to investigate the deformed gravity duals of these backgrounds on a wider swath of phase space, including non-integrable trajectories. The prototypical background is furnished by Sasaki-Einstein manifolds: AdS 5 ×Y p,q [51], where the method applied here can be used by generalizing the string solutions obtained in [52]. The un-deformed backgrounds are already known to be non-integrable [12,13].…”

Section: Discussionmentioning

confidence: 99%

On marginal deformations and non-integrability

Zayas

Zoubos

2014

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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 Poincaré 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.

“…The string solutions again show chaotic behavior implying nonintegrability of the corresponding sigma models. However, in Y p,q manifolds special care should be taken with the string solution to show that indeed they satisfy the Sasaki-Einstein constraints as in [15,16,17]. More recently it has been shown that integrability is not present in marginal complex β-deformations [18].…”

Section: Introduction and Methodsmentioning

confidence: 99%

Non-integrability in non-relativistic theories

Sfetsos

2014

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Generic non-relativistic theories giving rise to non-integrable string solutions are classified. Our analysis boils down to a simple algebraic condition for the scaling parameters of the metric. Particular cases are the Lifshitz and the anisotropic Lifshitz spacetimes, for which we find that for trivial dilaton dependence the only integrable physical theory is that for z = 1. For the hyperscaling violation theories we conclude that the vast majority of theories are non-integrable, while only for a small class of physical theories, where the Fermi surfaces belong to, integrability is not excluded. Schrödinger theories are also analyzed and a necessary condition for non-integrability is found. Our analysis is also applied to cases where the exponential of the dilaton is a monomial of the holographic coordinate.