Compactified rotating branes in the matrix model, and excitation spectrum towards one loop

We study compactified brane solutions of type R^4 x K in the IIB matrix model, and obtain explicitly the bosonic and fermionic fluctuation spectrum required to compute the one-loop effective action. We verify that the one-loop contributions are UV finite for R^4 x T^2, and supersymmetric for R^3 x S^1. The higher Kaluza-Klein modes are shown to have a gap in the presence of flux on T^2, and potential problems concerning stability are discussed.