  We consider the spectra of excitations around diagonal and intersecting
D-brane configurations on tori. These configurations are described by constant
curvature connections in a dual gauge theory description. The low-energy string
fluctuation spectrum is reproduced exactly by the gauge theory in the case of
vanishing field strength; however, this correspondence breaks down for fixed
nonzero field strength. We show that in many cases the full Born-Infeld action
correctly captures the low-energy spectrum in the case of non-vanishing field
strength. This gives a field theory description of the low-energy physics of
systems of diagonally wound branes and branes at angles as considered by
Berkooz, Douglas and Leigh. This description extends naturally to
non-supersymmetric configurations, where the tachyonic instability associated
with brane-anti-brane systems appears as an instability around a saddle point
solution of the corresponding Yang-Mills/Born-Infeld theory. In some cases, the
field theory description requires a non-abelian generalization of the
Born-Infeld action. We follow Tseytlin's recent proposal for formulating such
an action. In the case of intersecting branes, the non-abelian Born-Infeld
theory produces a transcendental relation which comes tantalizingly close to
reproducing the correct spectrum; however, a discrepancy remains which
indicates that a further clarification of the non-abelian Born-Infeld action
may be necessary.
