Waves, boosted branes and BPS states in M-theory

TL;DR

This paper explores the relationships between various BPS bound states in string theory and M-theory, revealing how certain bound states correspond to gravitational waves and boosted branes in 11-dimensional space, and establishing a link between string and membrane BPS spectra.

Contribution

It provides a detailed analysis of non-threshold BPS bound states in M-theory, relating them to gravitational waves and boosted branes, and connects string BPS states to supermembrane oscillations.

Findings

11D bound states correspond to gravitational waves and boosted branes.

The (q_1,q_2) string spectrum matches membrane BPS states.

Relations between boosted M-branes and supersymmetric bound states are established.

Abstract

Certain type II string non-threshold BPS bound states are shown to be related to non-static backgrounds in 11-dimensional theory. The 11-d counterpart of the bound state of NS-NS and R-R type IIB strings wound around a circle is a pure gravitational wave propagating along a generic cycle of 2-torus. The extremal (q_1,q_2) string with non-vanishing momentum along the circle (or infinitely boosted black string) corresponds in D=11 to a 2-brane wrapped around 2-torus with momentum flow along the (q_1,q_2) cycle. Applying duality transformations to the string-string solution we find type IIA background representing a bound state of 2-brane and 0-brane. Its lift to 11 dimensions is simply a 2-brane finitely boosted in transverse direction. This 11-d solution interpolates between a static 2-brane (zero boost) and a gravitational wave in 11-th dimension (infinite boost). Similar interpretations are given for various bound states involving 5-branes. Relations between transversely boosted M-branes and 1/2 supersymmetric non-threshold bound states 2+0 and 5+0 complement relations between M-branes with momentum in longitudinal direction and 1/4 supersymmetric threshold bound states 1+0 and 4+0. In the second part of the paper we establish the correspondence between the BPS states of type IIB strings on a circle and oscillating states of a fundamental supermembrane wrapped around a 2-torus. We show that the (q_1,q_2) string spectrum is reproduced by the membrane BPS spectrum, determined using a certain limit. This supports the picture suggested by Schwarz.