The symmetry algebras of Euclidean M-theory

TL;DR

This paper explores the structure of Euclidean supersymmetry algebras in D=11, revealing how quaternionic structures influence the algebra's central charges and implications for Euclidean supergravity.

Contribution

It provides a detailed analysis of Euclidean D=11 superalgebras, highlighting the role of quaternionic structures and complex conjugations in their formulation.

Findings

Identification of quaternionic structures in Euclidean D=11 supercharges

Relation between tensorial central charges and quaternionic structure

Implications for Euclidean supergravity theories

Abstract

We study the Euclidean supersymmetric D=11 M-algebras. We consider two such D=11 superalgebras: the first one is N=(1,1) self-conjugate complex-Hermitean, with 32 complex supercharges and 1024 real bosonic charges, the second is N=(1,0) complex-holomorphic, with 32 complex supercharges and 528 bosonic charges, which can be obtained by analytic continuation of known Minkowski M-algebra. Due to the Bott's periodicity, we study at first the generic D=3 Euclidean supersymmetry case. The role of complex and quaternionic structures for D=3 and D=11 Euclidean supersymmetry is elucidated. We show that the additional 1024-528=496 Euclidean tensorial central charges are related with the quaternionic structure of Euclidean D=11 supercharges, which in complex notation satisfy SU(2) pseudo-Majorana condition. We consider also the corresponding Osterwalder-Schrader conjugations as implying for N=(1,0) case the reality of Euclidean bosonic charges. Finally, we outline some consequences of our results, in particular for D=11 Euclidean supergravity.