Timelike T-Duality, de Sitter Space, Large $N$ Gauge Theories and Topological Field Theory

Abstract

T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type $II{B}^{\ast }$ theory and the IIB theory to a type $II{A}^{\ast }$ theory. The type $I{I}^{\ast }$ theories admit E-branes, which are the images of the type II D-branes under timelike T-duality and correspond to imposing Dirichlet boundary conditions in time as well as some of the spatial directions. The effective action describing an E$n$-brane is the $n$-dimensional Euclidean super-Yang-Mills theory obtained by dimensionally reducing 9+1 dimensional super-Yang-Mills on $9-n$ spatial dimensions and one time dimension. The $II{B}^{\ast }$ theory has a solution which is the product of 5-dimensional de Sitter space and a 5-hyperboloid, and the E4-brane corresponds to anon-singular complete solution which interpolates between this solution and flat space. This leads to a duality between the large $N$ limit of the Euclidean 4-dimensional U(N) super-Yang-Mills theory and the $II{B}^{\ast }$ string theory in de Sitter space, and both are invariant under the same de Sitter supergroup. This theory can be twisted to obtain a large $N$ topological gauge theory and its topological string theory dual. Flat space-time may be an unstable vacuum for the type $I{I}^{\ast }$ theories, but they have supersymmetric cosmological solutions.

47 pages, 1 Postscript figure, uses phyzzx macro. Monor corrections

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