Non-integrability of the $\Omega$-deformation

Abstract

We study integrability on the supergravity vacuum dual to the field theoretical $\Omega$-deformation of $\mathcal{N}=4$ super Yang-Mills theory. The deformation manifests itself as turning on a Kalb-Ramond field on the (Euclidean) AdS${}_5\times$S${}^5$, while the associated $H_3$ flux ignores half of the geometric isometries. By constructing appropriate string embeddings that incorporate the essential $H_3$ flux contribution on this background, we study their fluctuations through the associated Hamiltonian systems. Each and every case demonstrates that the string exhibits non-integrable dynamics, which in turn suggests that the $\Omega$-deformation does not preserve classical integrability.

6+2 pages

References in corpus (8)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On (non)integrability of classical strings in p-brane backgrounds
• Non-integrability in non-relativistic theories
• Integrability and Holographic Aspects of Six-Dimensional $\mathcal{N}=(1,0)$ Superconformal Field Theories
• Non-integrability and Chaos with Unquenched Flavor
• Analytic integrability for strings on $\eta$ and $\lambda$ deformed backgrounds
• Condition on Ramond-Ramond fluxes for factorization of worldsheet scattering in anti-de Sitter space
• Constraining integrable AdS/CFT with factorized scattering

Cited by in corpus (2)

• Non-integrability in AdS${}_3$ vacua
• Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA