Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix embeddings on flat $R^3$ and the geometry of membranes   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.

31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc