BPS Spectrum and Nahm Duality of Matrix Theory Compactifications

TL;DR

This paper explores the BPS bound states in Matrix theory compactified on 5, 6, and 7 dimensional tori, revealing dualities with black holes and strings via Nahm transformation.

Contribution

It demonstrates the relationship between flux and momentum multiplets of BPS states and black objects through Nahm duality in higher-dimensional torus compactifications.

Findings

BPS states correspond to black holes and strings via Nahm duality.

Flux multiplets relate to black holes, momentum multiplets to black strings.

Analysis extends to D-brane theories on dual tori.

Abstract

In the Matrix theories compactified on the $d$ dimensional torus with $d = 5, 6, 7$ which are described by the theories of D$d$-branes in the type IIA or IIB theory on the $d$ dimensional dual torus we analyze the BPS bound states of the background D$d$-brane with other objects by taking the matrix theory limit. Through the Nahm duality transformation the flux and the momentum multiplets for these BPS states are shown to be associated with the black holes and the black strings respectively from the viewpoint of the weakly coupled type IIA string theory compactified on the $d-1$ dimensional torus.