Only the sinusoidal quiver α(z)=A sin(ωz) in the new massive type IIA AdS5 family shows no chaotic signatures, providing suggestive evidence for its classical integrability.
Chaotic string dynamics in Bosonic $\eta$-deformed $AdS_5 \times T^{ 1,1}$ background
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abstract
We investigate a new class of $\eta$-deformed $AdS_5 \times T^{1,1}$ backgrounds produced by $r$-matrices that satisfy the modified classical Yang-Baxter equation [Jour. High Ener. Phys. 03 (2022) 094]. We examine the classical phase space of these (semi)classical strings by numerically studying the dynamics of the string sigma models over this deformed background, and we compute several chaos signals. These involve figuring out the Poincar'e section and computing the Lyapunov exponents. In the (semi)classical limit, we discover evidence that supports a non-integrable phase space dynamics.
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Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA
Only the sinusoidal quiver α(z)=A sin(ωz) in the new massive type IIA AdS5 family shows no chaotic signatures, providing suggestive evidence for its classical integrability.