2002/11/13 by K. Narayan, Narayan, K.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0211110
Latex, 34 pages incl. appendices, 4 EPS figures, v2. references added, v3. minor modifications
openalex publication_date 2002/11/13 · arxiv created 2003/09/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Drawing analogies with block spin techniques used to study continuum limits in critical phenomena, we attempt to block up D-branes by averaging over near neighbour elements of their (in general noncommuting) matrix coordinates, i.e. in a low energy description. We show that various D-brane (noncommutative) geometries arising in string theory appear to behave sensibly under blocking up, given certain key assumptions in particular involving gauge invariance. In particular, the (gauge-fixed) noncommutative plane, fuzzy sphere and torus exhibit a self-similar structure under blocking up, if some ``counterterm'' matrices are added to the resulting block-algebras. Applying these techniques to matrix representations of more general D-brane configurations, we find that blocking up averages over far-off-diagonal matrix elements and brings them in towards the diagonal, so that the matrices become ``less off-diagonal'' under this process. We describe heuristic scaling relations for the matrix elements under this process. Further, we show that blocking up does not appear to exhibit any ``chaotic'' behaviour, suggesting that there is sensible physics underlying such a matrix coarse-graining. We also discuss briefly interrelations of these ideas with B-fields and noncommutativity.