E_11: Sign of the times

TL;DR

This paper explores how the E_11 conjecture relates to different space-time signatures and gauge field signs, showing transformations connect various theories with multiple time dimensions, challenging traditional views on their physicality.

Contribution

It demonstrates that within E_11, different space-time signatures are connected via Weyl transformations, and argues against discarding theories with multiple time-directions.

Findings

Transformations connect (1,10) M-theory to (2,9) and (5,6) signatures.

Different signatures form disconnected orbits, indicating multiple possible physical theories.

The sign of the 4-form gauge field term is adjustable within the E_11 framework.

Abstract

We discuss the signature of space-time in the context of the E_11 -conjecture. In this setting, the space-time signature depends on the choice of basis for the ``gravitational sub-algebra'' A_10, and Weyl transformations connect interpretations with different signatures of space-time. Also the sign of the 4-form gauge field term in the Lagrangian enters as an adjustable sign in a generalized signature. Within E_11, the combination of space-time signature (1,10) with conventional sign for the 4-form term, appropriate to M-theory, can be transformed to the signatures (2,9) and (5,6) of Hull's M*- and M'-theories (as well as (6,5), (9,2) and (10,1)). Theories with other signatures organize in orbits disconnected from these theories. We argue that when taking E_11 seriously as a symmetry algebra, one cannot discard theories with multiple time-directions as unphysical. We also briefly explore links with the SL(32,R) conjecture.