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

TL;DR

This paper explores timelike T-duality leading to type IIB* theories with de Sitter solutions, establishing a duality with large N super-Yang-Mills and connecting to topological gauge theories and string duals.

Contribution

It introduces the concept of timelike T-duality resulting in type IIB* theories, and establishes a duality between Euclidean super-Yang-Mills and IIB* string theory in de Sitter space.

Findings

Type IIB* theories admit E-branes with Euclidean super-Yang-Mills descriptions.

A duality between large N super-Yang-Mills and IIB* in de Sitter space is established.

Topological gauge theories can be derived from twisting the large N super-Yang-Mills theory.

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.