Boundary State Analysis on the Equivalence of T-Duality and Nahm Transformation in Superstring Theory

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 4dimensional 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 RRsector 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. 1

Noncommutative Instantons Revisited

“…The spacial coordinates x µ has a Fock representation. To see this, introduce complex coordinates z 1 , z 2 by z 1 = x 2 + ix 1 and z 2 = x 4 + ix 3 . By using the complex coordinates, the noncommutativity is expressed as…”

“…Nahm transformations of explicit ASD gauge fields are performed in e.g. [1,16,20,43]. For surveys of the Nahm transformation, see e.g.…”

Exact construction of noncommutative instantons

“…Nahm transformations of explicit ASD gauge fields are performed in e.g. [2,22,27,54]. For surveys of the Nahm transformation, see e.g.…”

“…Combining these operators, the normalized solutionV = (V (1) ,V (2) ) is obtained in the following form.V…”

Nahm transformation and boundary state in T^2

“…We can define the Nahm transformation of U(N) gauge fields with first Chern number C 1 = k on T 2 [9,1]. This works as follows: Consider a bundle E → T 2 with a positive first Chern number, C 1 (E) = k > 0 and look for the zero modes of the Dirac operator,which is parametrized by the coordinatex of the dual torusT 2…”