Tachyon condensation in the D0/D4 system

TL;DR

This paper addresses tachyon condensation in a D0/D4 system with a NS B-field and analyzes the (0,4) string tachyon using Berkovits open superstring field theory. The zeroth-level tachyon potential is computed and shown to depend on the B-field, yielding a stationary point whose energy approximates the D0/D4 mass defect in three regimes of the B-field. The minimum accounts for about 70%, 62%, or 25% of the mass defect depending on the limit, highlighting the limitations of level-0 truncation in certain regimes. The tachyon condensate is interpreted as a noncommutative U(1) instanton, with the (0,4) strings decoupling from low-energy dynamics, consistent with the bound-state interpretation and ADHM construction.

Abstract

The D0/D4 system with a Neveu-Schwarz B-field in the spatial directions of the D4-brane has a tachyon in the spectrum of the (0,4) strings. The tachyon signals the instability of the system to form a bound state of the D0-brane with the D4-brane. We use the Wess-Zumino-Witten like open superstring field theory formulated by Berkovits to study the tachyon potential for this system. The tachyon potential lies outside the universality class of the D-brane anti-D-brane system. It is a function of the B-field. We calculate the tachyon potential at the zeroth level approximation. The minimum of the tachyon potential in this case is expected to reproduce the mass defect involved in the formation of the D0/D4 bound state. We compare the minimum of the tachyon potential with the mass defect in three cases. For small values of the B-field we obtain 70% of the expected mass defect. For large values of the B-field with Pf$(2πα' B) >0$ the potential reduces to that of the D-brane anti-D-brane reproducing 62% of the expected mass defect. For large values of the B-field with Pf$(2πα' B) <0$ the minimum of the tachyon potential gives 25% of the expected mass defect. At the tachyon condensate we show that the (0,4) strings decouple from the low energy dynamics.