Supersymmetry, p-brane duality and hidden space and time dimensions

TL;DR

The paper proposes a unified algebraic framework in which a globally extended 32-supercharge supersymmetry algebra in 12D with signature $(10,2)$, including p-form central charges, encodes both dualities and hidden higher-dimensional structures. Through toroidal compactifications and a detailed reclassification of charges under duality and hidden-symmetry groups, it links T-duality, U-duality, and hidden dimensions and illustrates this with a 4D example yielding $SU(8)$ and $E_{7(7)}$ structures. It further outlines a program to identify non-perturbative states by completing multiplets under a minimal compact group $K$ that bridges duality and hidden dimensions, potentially aligning with M-/F-theory frameworks. Overall, the work provides an algebraic, model-agnostic route to classify both perturbative and non-perturbative states and to understand how hidden dimensions and dualities shape the spectrum of a fundamental theory.

Abstract

A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions in a theory that treats $p$-branes democratically. The maximal number of dimensions is 12, with signature (10,2), containing one space and one time dimensions that are hidden from the point of view of perturbative 10-dimensional string theory or its compactifications. When the theory is compactified on $R^{d-1,1}\otimes T^{c+1,1}$ with $d+c+2=12,$ there are isometry groups that relate to the hidden dimensions as well as to duality. Their combined classification schemes provide some properties of non-perturbative states and their couplings.