Waves, boosted branes and BPS states in M-theory Original Research Article

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 a 2-torus. The extremal (q1, q2) string with non-vanishing momentum along the circle (or infinitely boosted black string) corresponds in D = 11 to a 2-brane wrapped around a 2-torus with momentum flow along the (q1, q2) cycle. Applying duality tranformations to the string-string solution we find the type IIA background representing the bound state of a 2-brane and a 0-brane. Its lift to 11 dimensions is simply a 2-brane finitely boosted in transverse direction. This 11D solution interpolates between a static 2-brane (zero boost) and a gravitational wave in 11th dimension (infinite boost). Similar interpretations are given for various bound states involving 5-branes. Relations between transversely boosted M-branes and 12 supersymmetric non-threshold bound states 2+0 and 5+0 complement those beteen M-branes with momentum in longitudinal direction and 14 supersymmetric threshold bound states 1+0 and 4+0. In the second part of the paper we establish the correspondence between 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 (q1, q2) string spectrum is reproduced by the membrane BPS spectrum, determined using a certain limit. This supports the picture suggested by Schwarz.