Nahm transformation and boundary state on T²

The T-duality for a bound state of a D2-D0 brane system and its equivalence with the Nahm transformation of the corresponding gauge theory on a 2-dimensional torus were investigated, using the boundary state analysis in superstring. Contrary to the case of a 4-dimensional torus, a nontrivial change in sign in a topological charge is obtained (which seems puzzling when regarded as a D-brane charge). It is shown that both approaches agree when a minus sign is included. The boundary state in the RR-sector is reformulated using a new representation of zeromodes, we show that the RR-coupling is invariant under T-duality. Finally, we show the T-duality invariance at the level of the Chern-Simon coupling by deriving the Buscher rule for the RR potentials (also known as the 'Hori formula'), including the correct sign.