From Black Holes Entropy to Consciousness: The Dimensions of the Brain Connectome

It has been shown that the theory of relativity can be applied physically to the functioning brain, so that the brain connectome should be considered as a four-dimensional spacetime entity curved by brain activity, just as gravity curves the four-dimensional spacetime of the physical world. Following the most recent developments in modern theoretical physics (black hole entropy, holographic principle, AdS/CFT duality), we conjecture that consciousness can naturally emerge from this four-dimensional brain connectome when a fifth dimension is considered, in the same way that gravity emerges from a 'flat' four-dimensional quantum world, without gravitation, present at the boundaries of a five-dimensional spacetime. This vision makes it possible to envisage quantitative signatures of consciousness based on the entropy of the connectome and the curvature of spacetime estimated from data obtained by fMRI in the resting state (nodal activity and functional connectivity) and constrained by the anatomical connectivity derived from diffusion tensor imaging.

The Kerr/CFT correspondence and its extensions

We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy's formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy's formula. We follow an effective field theory approach and consider the Kerr-Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.