String Theory Journal Club

Matrix geometries were introduced by J. Barrett in the spirit of Connes’ Noncommutative Geometry. As the name suggests, matrix geometries are modeled by finite dimensional algebras, which with additional structure form finite spectral triples (in some sense, an approximation to smooth manifolds). A path-integral quantization approach of these finite spectral triples turns out to lead to multi-matrix random models, the model in question being determined by the so-called spectral action. We present formulae for the spectral action of even-dimensional matrix geometries (as part of ongoing work).