2012/04/23 by David Berenstein, Eric Dzienkowski · 2 citations
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.86.086001
41 pages, 3 figures, uses revtex4-1. v2: references added, corrected an error in attribution of ideas
arxiv created 2012/04/23 · arxiv updated 2013/05/29
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 R3 using an index function defined for points in R3 that is constructed from the three matrices and the point. The set of surfaces is covariant under rotations, dilatations and translation operations on R3, 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.