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2015

AdS/CFT and the geometry of an energy gap

Hickling, Andrew, Wiseman, Toby

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We consider a CFT defined on a static metric that is the product of time with a smooth closed space of positive scalar curvature.

We expect the theory to exhibit an energy gap and our aim is to investigate how that gap depends on the geometry of the space.
For a free conformal scalar it is straightforward to show the gap normalised by the minimum value of the Ricci scalar of the space is minimised when the space is a sphere.
Our main result is then to show using geometric arguments that precisely the same result holds for fluctuations of a scalar operator in any holographic CFT.

AdS/CFT and the geometry of an energy gap · Around

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Note we have assumed the top-down model is second order in derivatives, and then the only curvature couplings to a scalar fluctuations can be via the ( D + 1 ) (D+1) -dimensional Ricci scalar which is constant and hence simply contributed to the mass

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