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

TL;DR

The paper introduces timelike T-duality, revealing IIB^* and IIA^* theories connected to ordinary type II theories via duality on timelike circles. It defines E-branes as timelike D-brane images with Euclidean worldvolume theories and shows a large-N duality between Euclidean 4D U(N) SYM and IIB^* on dS_5×H^5, supported by interpolating brane geometries. It analyzes the resulting ghostly RR sectors, Euclideanization, and the twistings of Euclidean SYM into topological theories, proposing a de Sitter holographic framework and a topological gravity limit. The work suggests rich connections between de Sitter holography, topological string theory, and twisted gauge/gravity dualities, with implications for stability, unitarity, and nonperturbative dynamics in timelike backgrounds.

Abstract

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