D-brane analyses for BPS mass spectra and U-duality

Abstract

We give a confirmation of U-duality of the type II superstring by discussing the mass spectrum of the BPS states. We first evaluate the mass spectrum of BPS solitons with one kind of R-R charges. Our analysis is based on the one-loop effective action of the D-brane, which is known as “Dirac-Born-Infeld (DBI) action”, and the fact that BPS states correspond to the SUSY cycles with minimal volumes. We show that the mass formula derived in this manner is completely fitted with that given by U-duality. We further discuss the cases of BPS solitons possessing several kinds of R-R charges. These are cases of “intersecting D-branes”, which cannot be described by simple DBI actions. We claim that, in these cases, higher loop corrections should be incorporated as binding energies between the branes. It is remarkable that the summation of the contributions from all loops reproduces the correct mass formula predicted by U-duality.