Duality and the Signature of Space-Time

TL;DR

The paper expands the landscape of M-theory and string theory beyond Lorentzian signatures by introducing $M^*$ and $M'$ in $(9,2)$ and $(6,5)$, along with Euclidean and star/prime variants of Type II theories. It develops timelike T-duality, derives duality relations that flip spacetime signatures, and identifies strong-coupling limits that decompactify extra timelike or spacelike dimensions, yielding a rich web of theories connected to the usual M-theory and Type II strings. Supersymmetry and fermion representations are analyzed across signatures, showing that a single underlying theory can yield multiple consistent real forms with 32 supercharges. The work maps out compactifications on tori and 3-tori, builds moduli-space diagrams, and discusses potential pathologies, arguing that duality can reconcile or reinterpret seemingly problematic features within a unified framework.

Abstract

Versions of M-theory are found in spacetime signatures (9,2) and (6,5), in addition to the usual M-theory in 10+1 dimensions, and these give rise to type IIA string theories in 10-dimensional spacetime signatures (10,0),(9,1),(8,2),(6,4) and (5,5), and to type IIB string theories in signatures (9,1),(7,3) and (5,5). The field theory limits are 10 and 11 dimensional supergravities in these signatures. These theories are all linked by duality transformations which can change the number of time dimensions as well as the number of space dimensions, so that each should be a different limit of the same underlying theory.