Spinors, superalgebras and the signature of space-time

TL;DR

This paper explores superconformal algebras across various space-time signatures, their real forms, and applications in supergravity theories with 32 supersymmetries, revealing three distinct phases based on norm states after dimensional reduction.

Contribution

It classifies superconformal algebras in different signatures and applies them to supergravities, connecting various theories and revealing phase structures in reduced models.

Findings

Different real forms of R-symmetries for various signatures.

Application to supergravities with 32 supersymmetries in dimensions up to 11.

Identification of three phases based on positive and negative norm states.

Abstract

Superconformal algebras embedding space-time in any dimension and signature are considered. Different real forms of the $R$-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than one times). Application of these superalgebras are found in the context of supergravities with 32 supersymmetries, in any dimension $D \leq 11$. These theories are related to $D = 11, M, M^*$ and $M^\prime$ theories or $D = 10$, IIB, IIB$^*$ theories when compactified on Lorentzian tori. All dimensionally reduced theories fall in three distinct phases specified by the number of (128 bosonic) positive and negative norm states: $(n^+,n^-) = (128,0), (64,64), (72,56)$.