M-Theory Solutions in Multiple Signatures from E_11

TL;DR

This paper extends the E_11 solution generating group to general weights, producing M-theory solutions across multiple spacetime signatures and rediscovering known S-brane solutions through symmetry transformations.

Contribution

It generalizes the E_11 solution generating method to arbitrary weights, enabling the construction of M-theory solutions in various signatures and connecting to known S-brane solutions.

Findings

Solutions in signatures (1,10), (2,9), (5,6), (6,5), (9,2), (10,1)

Signature transformations via Weyl reflections

Reinterpretation of known S-brane solutions

Abstract

We generalise the previously given E_11 half BPS solution generating group element to general weights of A_10. We find that it leads to solutions of M-theory but in signatures (1,10), (2,9), (5,6), (6,5), (9,2) and (10,1). The signature transformations of the solution are naturally generated by the Weyl reflections required to transform the lowest A_10 weight into a general weight in the same representation. We also rediscover known S-brane solutions in M-theory from the group element in different signatures.