Mon, 23 Oct 2006
12:00
L3

Einstein Geometry and Conformal Field Theory

James Sparks
(Oxford)
Abstract
I shall describe two recent results in Sasaki-Einstein geometry, which is the odd-dimensional cousin of Kahler-Einstein geometry, and how they are related to four-dimensional superconformal field theory (SCFT) via the AdS/CFT correspondence. The first is a proof that the volumes of such Einstein manifolds are always algebraic numbers, which reflects a similar statement about central charges in SCFTs due to Intriligator and Wecht. The second descibes two simple holomorphic obstructions to the existence of such Einstein metrics. In such obstructed cases the non-existence of the dual superconformal fixed point may be proven by a simle application of the unitarity bound and the “a-theorem”, respectively, and these may be related directly to the geometrical obstructions via AdS/CFT arguments. On the mathematical side, these are new simple obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.

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