Exact description of D-branes via tachyon condensation

Abstract

We examine the fluctuations around a Dp-brane solution in an unstable D-brane system using boundary states and also boundary string field theory. We show that the fluctuations correctly reproduce the fields on the Dp-brane. Plugging these into the action of the unstable D-brane system, we recover not only the tension and RR charge, but also full effective action of the Dp-brane exactly. Our method works for general unstable D-brane systems and provides a simple proof of D-brane descent/ascent relations under the tachyon condensation. In the lowest dimensional unstable D-brane system, called K-matrix theory, D-branes are described in terms of operator algebra. We show the equivalence of the geometric and algebraic descriptions of a D-brane world-volume manifold using the equivalence between path integral and operator formulation of the boundary quantum mechanics. As a corollary, the Atiyah-Singer index theorem is naturally obtained by looking at the coupling to RR-fields. We also generalize the argument to type I string theory.

Geometry from matrices via D-branes

“…Indeed, in [23,24], we showed that the decent relations and the ascent relations exactly, i.e. the equivalences between the boundary state of the unstable Dp-brane system and the one of the BPS Dq-brane.…”

“…the equivalences between the boundary state of the unstable Dp-brane system and the one of the BPS Dq-brane. Using [23,24], the diagonalization of the tachyon gives the equivalence between the boundary state of the D0-branes and the one of the D2-brane explicitly, where all the string scale l s corrections are included. This method was applied to the Nahm equation [25], ADHM construction of instantons [26], the supertubes [27] and Nahm transformation [28].…”

Ramond-Ramond couplings of D-branes

“…For this, it would be more convenient to use following another definition of the conjugate acting trivially on the forms: (dx µ 1 · · · dx µn ) † = (dx µ 1 · · · dx µn ). With this and the non-trivial factor appeared in the transformation from A toÃ, we see that The generalization to the Dp-antiDp brane system can be done following [5,19] with the T-dualized formula. In this system the RR-charges are known to be generated by the ascent relation [57,58] by the tachyon condensation and there would be analogue of this for the massive fields.…”

“…Taking this effect into account, instead of (4.11), we will have 12) where * represents the fermionic * -product defined in [19]. Thus, the gauge transformation is given by…”

“…For the evaluation of the Γ integral, we can use the identity shown in [19] DΓ e dτ dθ 1 21) where M(Γ) = M 0 (Γ) + θM 1 (Γ) in which only the superfield X was decomposed to the component fields. Here the r.h.s.…”