Along holographic RG flows, the acceleration of spread complexity and the covariant c-function are algebraically related: inversely in fixed-dimension domain walls and Dp-branes, co-monotonically in twisted compactifications.
Consistent Type IIB Reductions to Maximal 5D Supergravity
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abstract
We use exceptional field theory as a tool to work out the full non-linear reduction ansaetze for the AdS$_5\times S^5$ compactification of IIB supergravity and its non-compact counterparts in which the sphere $S^5$ is replaced by the inhomogeneous hyperboloidal space $H^{p,q}$. The resulting theories are the maximal 5D supergravities with gauge groups SO(p,q). They are consistent truncations in the sense that every solution of 5D supergravity lifts to a solution of IIB supergravity. In particular, every stationary point and every holographic RG flow of the scalar potentials for the compact and non-compact 5D gaugings directly lift to solutions of IIB supergravity.
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Krylov Complexity and $c$-function along RG Flows
Along holographic RG flows, the acceleration of spread complexity and the covariant c-function are algebraically related: inversely in fixed-dimension domain walls and Dp-branes, co-monotonically in twisted compactifications.