# Blocking up D-branes : Matrix renormalization ? Source: [Blocking up D-branes : Matrix renormalization ?]() Collection index: [llms.txt]() Data updated: 2025-10-23T17:50:26.499Z Authors: K. Narayan Published: 2002-11-13T01:57:38.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()