Non-Integrability of Strings in AdS6×S2×ΣAdS_{6}\times S^{2}\times\Sigma Background and its 5D Holographic Duals

In this manuscript we study Liouvillian non-integrability of strings in $AdS_{6}\times S^{2}\times\Sigma$ background and its 5D Holographic Duals. For this we consider soliton strings and look for simple solutions in order to reduce our equations to only one linear second order differential equation called NVE(normal variation equation ). We show that, differently of previous studies, the correct truncation is given by $\eta=0$ and not $\sigma=0$. With this we are able to study many recent cases considered in the literature: the abelian and non-abelian T-duals, the $(p,q)$-five-brane system, the T$_{N}$,+$_{MN}$ theories and the $\tilde{T}_{N,P}$ and $+_{P,N}$ quivers. We show that all of them, and therefore the respective field theory duals, are not integrable. Finally, we consider the general case at the boundary $\eta=0$ and show that we can get general conclusions about integrability. For example, beyond the above quivers, we show generically that long quivers are not integrable.Comment: 28 page

Topological gravity localization on a delta-function like Brane

Besides the String Theory context, the quantum General Relativity can be studied by the use of constrained topological field theories. In the celebrated Plebanski formalism, the constraints connecting topological field theories and gravity are imposed in space-times with trivial topology. In the braneworld context there are two distinct regions of the space-time, namely, the bulk and the braneworld volume. In this work we show how to construct topological gravity in a scenario containing one extra dimension and a delta-function like 3-brane which naturally emerges from a spontaneously broken discrete symmetry. Starting from a D=5 theory we obtain the action for General Relativity in the Palatini form in the bulk as well as in the braneworld volume. This result is important for future insights about quantum gravity in brane scenarios.Comment: 4 page