Strings Group Meeting

Using techniques originating in a certain approach to Clifford bundles known as "geometric algebra", I discuss a geometric reformulation of constrained generalized Killing spinor equations which proves to be particularly effective in the study and classification of supersymmetric flux compactifications of string and M-theory. As an application, I discuss the most general N=2 compactifications of M-theory to three dimensions, which were never studied in full generality before. I also touch upon the connection of such techniques with a certain variant of the quantization of spin systems.

In an anisotropic limit of the weakly-coupled, 2+1-dimensional non-Abelian gauge theories are equivalent to a collection of integrable 1+1-dimensional quantum field theories. This fact makes it possible to understand confinement near this limit. Using exact form factors, it is possible to study the theory away from the extreme anisotropic limit. The string tension between fundamental color sources is found. Adjoint sources are not confined. Some ideas concerning the isotropic case and the generalization to 3+1 dimensions will be discussed.