Non-integrability on AdS$_3$ supergravity backgrounds

Understand

We investigate classical integrability on two recently discovered classes of backgrounds in massive IIA supergravity.

• These vacua are of the form AdS$_3\times\,$S$^2\times\mathbb{R}\times\,$CY$_2$, they preserve small $\mathcal{N}=(0,4)$ supersymmetry and are associated with D8$-$D6$-$D4$-$D2 Hanany-Witten brane set-ups.
• We choose an appropriate string embedding and use differential Galois theory on its associated Hamiltonian system, intending to produce the conditions under which Liouvillian solutions may occur.
• By constraining the parameters of the system according to the consistency of the associate brane set-ups we prove that no such conditions exist, yielding the complete non-integrability of these vacua.