Boundary state analysis on the equivalence of T-duality and Nahm transformation in superstring theory

TL;DR

This paper demonstrates the equivalence of T-duality and Nahm transformation in superstring theory through boundary state analysis, clarifying sign issues and invariance of RR-couplings on a 2D torus.

Contribution

It reformulates boundary states in the RR-sector and proves T-duality invariance of RR-couplings and Chern-Simons terms, resolving sign ambiguities.

Findings

T-duality corresponds to Nahm transformation on a 2D torus.

RR-coupling invariance under T-duality is confirmed.

The Buscher rule for RR-potentials is derived with correct signs.

Abstract

We investigated the equivalence of the T-duality for a bound state of D2 and D0-branes with the Nahm transformation of the corresponding gauge theory on a 2-dimensional torus, using the boundary state analysis in superstring theory. In contrast to the case of a 4-dimensional torus, it changes a sign in a topological charge, which seems puzzling when regarded as a D-brane charge. Nevertheless, it is shown that it agrees with the T-duality of the boundary state, including a minus sign. We reformulated boundary states in the RR-sector using a new representation of zeromodes, and show that the RR-coupling is invariant under the T-duality. Finally, the T-duality invariance at the level of the Chern-Simon coupling is shown by deriving the Buscher rule for the RR-potentials, known as the 'Hori formula', including the correct sign.