Tachyon Condensation in Superstring Field Theory

TL;DR

The paper tests the tachyon condensation conjecture within a Wess–Zumino–Witten–like open superstring field theory, focusing on brane–antibrane and non-BPS D-branes. Using a level-truncation scheme and a twist-even truncation in the NS sector, the authors compute the tachyon potential up to level three, obtaining $85\%$ of the brane tension cancellation at the potential minimum and demonstrating a bounded-below potential with two degenerate vacua. They also analyze a tachyonic kink on a non-BPS D-string, finding an energy close to the tension of a lower-dimensional D-brane, $E \approx 1.03\,\mathcal{T}_0$, within the crude kinetic-term approximation. Overall, the results provide nontrivial evidence that the open superstring field theory description captures tachyon condensation consistently and exhibits convergence toward the expected closed-string vacuum, while suggesting avenues for higher-level computations and deeper understanding of the tachyon vacuum.

Abstract

It has been conjectured that at the stationary point of the tachyon potential for the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess-Zumino-Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by condensation of the tachyon field alone. While the action is non-polynomial, the multiscalar tachyon potential to any fixed level involves only a finite number of interactions. We compute this potential to level three, obtaining 85% of the expected vacuum energy, a result consistent with convergence that can also be viewed as a successful test of the string field theory. The resulting effective tachyon potential is bounded below and has two degenerate global minima. We calculate the energy density of the kink solution interpolating between these minima finding good agreement with the tension of the D-brane of one lower dimension.

Figures (1)

• Figure 1: The tachyon potential $v(t)=V(t)/M$ given in (\ref{['epot1']}) (solid line). For reference we also show the zeroeth order potential (dashed line).