Branes, Weights and Central Charges

TL;DR

This paper analyzes half-supersymmetric branes in string theory using group theory, revealing their association with the longest weights of U-duality representations and exploring the properties of standard and non-standard branes.

Contribution

It provides a group-theoretical framework for classifying branes, calculates degeneracies of non-standard branes, and describes U-duality invariants for multi-charge configurations.

Findings

Half-supersymmetric branes linked to longest weights of U-duality representations.

Degeneracy of BPS conditions for non-standard branes calculated.

U-duality invariants for multi-charge non-standard brane orbits derived.

Abstract

We study the properties of half-supersymmetric branes in string theory with 32 supercharges from a purely group-theoretical point of view using the U-duality symmetry of maximal supergravity and the R-symmetry of the corresponding supersymmetry algebra. In particular, we show that half-supersymmetric branes are always associated to the longest weights of the U-duality representation of the potentials coupling to them. We compare the features of branes with three or more transverse directions (that we call "standard" branes) to those with two or less transverse directions (that we denominate "non-standard" branes). We show why the BPS condition of the non-standard branes is in general degenerate and for each case we calculate this degeneracy. We furthermore show how the orbits of multi-charge configurations of non-standard branes can be calculated and give the U-duality invariants describing these orbits. We show that different orbits of non-standard branes can have the same BPS condition.