Timelike T-duality, de Sitter space, large \(N\) gauge theories and topological field theory

DOI10.1088/1126-6708/1998/07/021zbMATH Open0958.81085arXivhep-th/9806146OpenAlexW3098624600MaRDI QIDQ1588122

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Publication date: 3 December 2000

Published in: (Search for Journal in Brave)

Abstract: T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type $II{B}^{*}$ theory and the IIB theory to a type $II{A}^{*}$ theory. The type $I{I}^{*}$ 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 $II{B}^{*}$ 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 $II{B}^{*}$ 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 $I{I}^{*}$ theories, but they have supersymmetric cosmological solutions.

Full work available at URL: https://arxiv.org/abs/hep-th/9806146

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