The non-Integrability of Strings in Massive Type IIA and their Holographic duals

TL;DR

The study establishes non‑integrability for a class of six‑dimensional ${\rm N}=(1,0)$ SCFTs realized holographically in Massive IIA by analyzing semi‑classical string solitons on $AdS_7\times M_3$. Using Kovacic's algorithm on the Normal Variational Equation and comprehensive numerical chaos diagnostics (Lyapunov exponents, power spectra, and Poincaré sections), the authors demonstrate Liouville non‑integrability in the dual CFT sectors. The holographic backgrounds are constructed from a master function ${\boldsymbol{\alpha}}(z)$ and organized into explicit quivers, with central charges that scale as $c\sim N^2P^5$ for long quivers, corroborating substantial degrees of freedom. The results provide a concrete holographic route to probe the long‑operator dynamics of these 6d SCFTs and suggest broad implications for chaos and integrability in higher‑dimensional holographic CFTs.

Abstract

In this work we study various aspects of six-dimensional ${\cal N}=(1,0)$ SCFTs. We consider the construction of their string duals in Massive IIA and discuss some observables in given examples. We study the dynamics of string solitons wrapping and rotating on the Massive IIA background and show that the associated Hamiltonian system is both non-integrable and chaotic, implying the non-integrability of the dual CFT. Our procedure is analytic, using well developed mathematical techniques, and numerical, by the explicit calculation of power spectra, Lyapunov coefficients and Poincaré sections.

Figures (19)

• Figure 1: The quiver encoding the dynamics of our first example CFT.
• Figure 2: The function $\hat{\alpha}(z) \equiv \frac{\alpha(z)}{81 \pi^2 N}$ and its derivatives, that describe the CFT associated with the quiver in Figure \ref{['figure1xx']}.
• Figure 3: From top-left to bottom-right, the functions $f_1(z),...., f_6(z)$, that describe the CFT associated with the quiver in Figure \ref{['figure1xx']}.
• Figure 4: The Ricci scalar associated to the quiver in Figure \ref{['figure1xx']}.
• Figure 5: The quiver encoding the dynamics of our second example CFT.