D-branes as Tachyon Lumps in String Field Theory

TL;DR

The authors test the conjecture that tachyon lumps on open bosonic string field theory describe D-branes of one lower dimension by placing the lump on a circle of radius $R$ and applying a modified level expansion to systematically include higher-derivative effects. They develop a background-independent string field framework and a level $(M,N)$ truncation that accommodates momentum along the lump direction, enabling controlled computations of the lump's mass and profile; the lump mass is compared to the lower-dimensional D-brane tension via the ratio $r=E_{lump}/\mathcal{T}_0$ with two practical estimators $r^{(1)}$ and $r^{(2)}$. For select radii (notably $R=\sqrt{3}$), the results yield lump masses within about 1% of the expected D-brane tension, and a definite lump profile is observed with a Gaussian fit giving a 6-sigma size of $9.3\sqrt{\alpha'}$, indicating the lump is a fat but well-defined object. The method naturally introduces UV and IR cutoffs, suggesting a viable route to quantum string field theory, and it generalizes to other radii and potentially to higher codimensions and NS sectors, with several open questions noted for future work.

Abstract

It has been conjectured that the tachyonic lump solution of the open bosonic string field theory describing a D-brane represents a D-brane of one lower dimension. We place the lump on a circle of finite radius and develop a variant of the level expansion scheme that allows systematic account of all higher derivative terms in the string field theory action, and gives a calculational scheme that can be carried to arbitrary accuracy. Using this approach we obtain lump masses that agree with expected D-brane masses to an accuracy of about 1%. We find convincing evidence that in string field theory the lump representing a D-brane is an extended object with a definite profile. A gaussian fit to the lump gives a 6-sigma size of 9.3 \sqrt{α'}. The level truncation scheme developed here naturally gives rise to an infrared and ultraviolet cut-off, and may be useful in the study of quantum string field theory.

Figures (8)

• Figure 1: The dashed line shows a plot of $t(x)$ for $R=\sqrt{3}$ at level (1/3, 2/3) approximation. The solid line shows the plot of $t(x)$ for $R=\sqrt{3}$ at the level (3,6) approximation.
• Figure 2: The dashed line shows a plot of $t(x)$ for $R=\sqrt{3}$ at level (4/3, 8/3) approximation. The solid line shows the plot of $t(x)$ for $R=\sqrt{3}$ at the level (3,6) approximation.
• Figure 3: The dashed line shows a plot of $t(x)$ for $R=\sqrt{3}$ at level (2, 4) approximation. The solid line shows the plot of $t(x)$ for $R=\sqrt{3}$ at the level (3,6) approximation.
• Figure 4: The dashed line shows a plot of $t(x)$ for $R=\sqrt{3}$ at level (7/3, 14/3) approximation. The solid line shows the plot of $t(x)$ for $R=\sqrt{3}$ at the level (3,6) approximation.
• Figure 5: The dashed line shows a plot of $t(x)$ for $R=\sqrt{15/2}$ at level (32/15, 64/15) approximation. The solid line spanning a smaller range of $x$ shows the plot of $t(x)$ for the level (3,6) approximation at $R=\sqrt{3}$.