Supersymmetric Branes in the Matrix Model of PP Wave Background
Dongsu Bak
TL;DR
The paper analyzes the matrix model in a pp-wave background and constructs supersymmetric brane configurations beyond the well-known fuzzy sphere. It identifies two main branches: rotating ellipsoidal membranes preserving $8$ real supercharges and a general rotating hyperbolic membrane preserving $1/8$ (rising to $1/4$ when angular momentum vanishes), with hyperbolic shapes described by $SO(2,1)$ representations. The author computes worldvolume fluctuations on these branes and shows there are no massless transverse modes on the hyperbolic branes, additionally deriving the $0$–$2$ string spectra; static hyperbolic branes are classified by unitary $SO(2,1)$ representations, yielding explicit mass spectra for fluctuations and inter-brane strings. These results illuminate nonperturbative brane dynamics in the pp-wave matrix model and motivate a systematic approach to BPS state classification in massive matrix theories, as well as further exploration of D0–brane interactions in this background.
Abstract
We consider the matrix model associated with pp-wave background and construct supersymmetric branes. In addition to the spherical membrane preserving 16 supersymmetries, one may construct rotating elliptic membranes preserving 8 supersymmetries. The other branch describes rotating 1/8 BPS hyperbolic branes in general. When the angular momentum vanishes in this branch, the hyperbolic brane becomes 1/4 BPS preserving 8 real supersymmetries. It may have the shape of hyperboloid of one or two sheets embedded in the flat three space. We study the spectrum of the worldvolume fields on the hyperbolic branes and show that there are no massless degrees. We also compute the spectrum of the 0-2 strings.