Matrix embeddings on flat $R^3$ and the geometry of membranes

Details Matrix embeddings on flat $R^3$ and the geometry of membranes Matrix embeddings on flat $R^3$ and the geometry of membranes

2012-04-12

arxiv.org/abs/1204.2788v2

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, 3 figures, uses revtex4-1. v2: references added, corrected an error in attribution of ideas

Scientific paper

We show that given three hermitian matrices, what one could call a fuzzy representation of a membrane, there is a well defined procedure to define a set of oriented Riemann surfaces embedded in $R^3$ using an index function defined for points in $R^3$ that is constructed from the three matrices and the point. The set of surfaces is covariant under rotations, dilatations and translation operations on $R^3$, it is additive on direct sums and the orientation of the surfaces is reversed by complex conjugation of the matrices. The index we build is closely related to the Hanany-Witten effect. We also show that the surfaces carry information of a line bundle with connection on them. We discuss applications of these ideas to the study of holographic matrix models and black hole dynamics.

Affiliated with

Also associated with

No associations

Rating

Matrix embeddings on flat $R^3$ and the geometry of membranes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Matrix embeddings on flat $R^3$ and the geometry of membranes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Matrix embeddings on flat $R^3$ and the geometry of membranes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-313160