Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds

Abstract

We show that the string worldsheet theory of Gaiotto-Maldacena holographic duals to N=2 superconformal field theories generically fails to be classically integrable. We demonstrate numerically that the dynamics of a winding string configuration possesses a non-vanishing Lyapunov exponent. Furthermore an analytic study of the Normal Variational Equation fails to yield a Liouvillian solution. An exception to the generic non-integrability of such backgrounds is provided by the non-Abelian T-dual of $Ad{S}_5\times S^5$. Here by virtue of the canonical transformation nature of the T-duality classical integrability is known to be present.

20 pages plus appendices. Various figures. References added

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Cited by in corpus (36)

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• ${\text{AdS}}_2\times {\text{S}}^2\times {\text{CY}}_2$ solutions in Type IIB with 8 supersymmetries
• Non-integrability on AdS${}_3$ supergravity backgrounds
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• Electrostatic description of 3d $\mathcal{N}=4$ linear quivers
• Holographic description of SCFT${}_5$ compactifications
• Nonrelativistic pulsating strings
• Consistent truncations of supergravity and $\frac{1}{2}$-BPS RG flows in $4d$ SCFTs
• Non-integrability in AdS${}_3$ vacua
• Holography for 2d $\mathcal{N}=(0,4)$ quantum field theory
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Chaotic spin chains in AdS/CFT
• Constraining integrable AdS/CFT with factorized scattering
• Spin-2 excitations in Gaiotto-Maldacena solutions
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• Circular string in a Black p-brane leading to chaos
• Linear Quivers at Large-$N$
• Fragmentation and defragmentation of strings in type IIA and their holographic duals
• Integrability and non-integrability for marginal deformations of 4d $\mathcal{N}=2$ SCFTs
• Non-integrability of the $\Omega$-deformation
• Analytic Non-Integrability and S-Matrix Factorization
• Non-integrability for $\mathcal{N}=1$ SCFTs in $5d$
• Spin-$2$ operators in AdS${}_2$/CFT${}_1$
• Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA
• Correlation functions for open strings and chaos
• Analytic integrability for holographic duals with $J\bar{T}$ deformations
• Complexity and Operator Growth in Holographic 6d SCFTs
• Integrability and non-integrability for holographic dual of Matrix model and non-Abelian T-dual of AdS${}_5\times$S${}^5$
• Analytic (non)integrability of Arutyunov-Bassi-Lacroix model
• Newton-Cartan $D0$ branes from $D1$ branes and integrability
• Holographic timelike entanglement and $c$ theorem for supersymmetric QFTs in ($0+1$)d
• Nonrelativistic strings and the limits of $\mathcal{N}=2$ dualities
• Holographic zero sound for $\mathcal{N}=2$ SCFTs in 4d
• Factorised scattering and (non)integrability for marginally deformed $Ad{S}_5/CF{T}_4$