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arXiv · 1912.03791

Non-integrability of the $\Omega$-deformation

Kostas Filippas
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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.

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Kostas Filippas. 2019-12-09. Non-integrability of the $\Omega$-deformation. https://doi.org/10.1103/physrevd.101.046025

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