One-loop corrections to $η/s$ in AdS$_4$/CFT$_3$

We study quantum corrections at one-loop order to the shear viscosity to entropy ratio by implementing the Vilkovisky-Barvinsky effective action in asymptotically Anti-de Sitter spacetimes. The shear viscosity is shown to receive no corrections at this order, but the entropy acquires a logarithmic correction. The coefficient of this logarithm turns out to depend on the spin of the particles running in the loop and it can be either positive or negative. On the basis of this result, we argue that the Kovtun-Son-Starinets bound cannot be seen as a fundamental property of nature beyond the classical regime.

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