Descent Relations Among Bosonic D-branes

TL;DR

The paper addresses how bosonic D-branes of different dimensionalities are related through tachyon condensation by showing that a tachyonic kink on a pair of coincident D-$p$-branes is equivalent to a D-$(p-1)$-brane. It uses a circle compactification with a half-unit Wilson line to trigger a massless tachyon mode at the critical radius $R_c= frac{1}{2}$, enabling a exactly marginal BCFT deformation that interpolates to the D-$(p-1)$-brane description; via T-duality and a careful analysis of the spectrum, it demonstrates that the kink on the circle corresponds to a D-particle in the $R orac{1}{2}$ and ultimately in the $R o o o o o o o o o o o$ Minkowski space. The study also presents a lump-based perspective on the D-particle by showing a single D-string can host a tachyonic lump equivalent to the D-particle, and reconciles these views through a 2×2 tachyon matrix and a U(2) gauge transformation. Together, the results establish a consistent descent relation and unify kink- and lump-based pictures within a bosonic-string BCFT framework, extending the understanding of D-brane descent and open-string tachyon dynamics.

Abstract

We show that the tachyonic kink solution on a pair of D-p-branes in the bosonic string theory can be identified with the D-(p-1)-brane of the same theory. We also speculate on the possibility of obtaining the D-(p-1)-brane as a tachyonic lump on a single D-p-brane. We suggest a possible reinterpretation of the first result which unifies these two apparently different descriptions of the D-(p-1) brane.

Figures (8)

• Figure 1: The tachyonic kink on the pair of D-$p$-branes.
• Figure 2: The tachyonic kink on the pair of D-strings on a circle.
• Figure 3: The marginal flow in the $R-\alpha$ plane interpolating between a pair of D-strings and a D-particle.
• Figure 4: The tachyon field on the D-string which produces a pair of D-particles.
• Figure 5: The tachyonic lump on a D-string, representing a single D-particle.