On Clifford-Algebraic "Holoraumy", Dimensional Extension, and SUSY Holography

TL;DR

This paper introduces a novel concept called 'holoraumy' derived from automorphisms of supersymmetry algebras, revealing how 0-brane supermultiplets encode higher-dimensional spacetime geometry through their transformations.

Contribution

It defines and explores 'holoraumy' as a new geometric structure in supersymmetry, linking world-line supermultiplets to higher-dimensional Lorentz transformations and holographic spacetime information.

Findings

Holoraumy extends holonomy and curvature concepts in supersymmetry.

0-brane supermultiplets encode higher-dimensional Lorentz transformations.

Spin(3) generators are represented within holoraumy tensors.

Abstract

We analyze the group of maximal automorphisms of the $N$-extended world-line supersymmetry algebra, and its action on off-shell supermultiplets. This defines a concept of "holoraumy" that extends the notions of holonomy and curvature in a novel way and provides information about the geometry of the supermultiplet field-space. In turn, the "holoraumy" transformations of 0-brane dimensionally reduced supermultiplets provide information about Lorentz transformations in the higher-dimensional spacetime from which the 0-brane supermultiplets are descended. Specifically, Spin(3) generators are encoded within 0-brane "holoraumy" tensors. World-line supermultiplets are thus able to holographically encrypt information about higher dimensional spacetime geometry.