Flux stabilization in compact groups

We consider the Born-Infeld action for symmetry-preserving, orientable D-branes in compact group manifolds. We find classical solutions that obey the flux quantization condition. They correspond to conformally invariant boundary conditions on the world sheet. We compute the spectrum of quadratic fluctuations and find agreement with the predictions of conformal field theory, up to a missing level-dependent truncation. Our results extend to D-branes with the geometry of twined conjugacy classes; they illustrate the mechanism of flux stabilization of D-branes.