Blocking up D-branes : Matrix renormalization ?

TL;DRAbstract

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 el

Chat with Paper

AI Agents for this Paper