D0-D4 brane tachyon condensation to a BPS state and its excitation spectrum in noncommutative super Yang-Mills theory

We investigate theD0-D4-brane system for differentB-field backgrounds including the small instanton singularity in noncommutative SYM theory. We discuss the excitation spectrum of the unstable state as well as for the BPS D0-D4 bound state. We compute the tachyon potential which reproduces the complete mass defect. The relevant degrees of freedom are the massless (4, 4) strings. Both results are in contrast with existing string field theory calculations. The excitation spectrum of the small instanton is found to be equal to the excitation spectrum of the fluxon solution on Rθ×R which we trace back to T -duality. For the effective theory of the (0, 0) string excitations we obtain a BFSS matrix model. The number of states in the instanton background changes significantly when the B-field becomes selfdual. This leads us to the proposal of the existence of a phase transition or cross over at self-dual B-field. ∗ [email protected]