Seminar series
Date
Mon, 23 Oct 2006
12:00
12:00
Location
L3
Speaker
James Sparks
Organisation
Oxford
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.
/notices/events/abstracts/string-theory/mt06/sparks.shtml