Special holonomy spaces in M/String theory and supergravity
Speaker(s): Lilia Anguelova
Abstract: Special holonomy spaces play a prominent role in supersymmetric theories. In this talk two different physical problems will be considered which however are related mathematically via the properties of a class of Quaternion-Kahler spaces (called toric) which have two commuting U(1) isometries. The first problem is M-theory on G_2 holonomy spaces. As is known for a long time now, compactifications of 11-dimensional supergravity (which is the low energy limit of the fundamental 11-dimensional theory that I will refer to as M-theory) on smooth G_2 holonomy spaces give N=1 supersymmetry in four dimensions but no nonabelian gauge fields and no chiral fermions. Both problems can be resolved by considering singular G_2 spaces. We will use toric Quaternion-Kahler spaces to write down infinitely many new G_2 metrics. We will classify the singularities that occur in those spaces and also study the dual type IIA and IIB backgrounds that M-theory on those spaces has due to the two U(1) isometries. The other physical problem is related to N=2 Supergravity in 5 dimensions. This theory drew a lot of attention lately due to at least two different reasons. One is that it gives the effective description of the compactification to 5 dimensions of Horava-Witten theory which is thought to have played a role in the early universe. Another is the attempt to embed the Randall-Sundrum scenario in a consistent fundamental theory. As a first step toward that goal is the embedding in N=2, D=5 Supergravity. There have appeared no-go theorems for such an embedding. By using toric Quaternion-Kahler spaces as targets for the scalars of a single hypermultiplet coupled to the sugra multiplet in 5 dimensions, we find infinitely many counterexamples to these no-go theorems.
Date: 18/02/2003 - 4:00 pm
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