Tachyon condensation in cubic superstring field theory

TL;DR

The paper investigates tachyon condensation on non-BPS D-branes within cubic superstring field theory by employing a 0-picture formulation with a double-step inverse picture changing operator $Y_{-2}$. It performs level-truncated computations of the tachyon potential at $(1/2,1)$ and $(2,6)$, deriving explicit effective potentials and locating their minima. The results show minima corresponding to $V_{\mathrm{min}} ≈ -0.975\,\taũ_p$ and $V_{\mathrm{min}} ≈ -1.058\,\taũ_p$, i.e., 97.5% and 105.8% of the non-BPS D$p$-brane tension, illustrating that Sen's conjecture is supported within this framework though convergence is not monotone. The analysis clarifies tension normalization and the impact of superghost normalization on the brane tension, reinforcing the role of tachyon condensation in brane decay scenarios.

Abstract

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane-anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case we obtain that the value of the potential at the minimum is 97.5% of the non BPS D-brane tension. Using a special gauge in the second case we get 105.8% of the tension.

Figures (3)

• Figure 1: The maps for Witten's vertex.
• Figure 2: The system of two non BPS D$p$-branes and strings attached to them.
• Figure 3: Graphics of the tachyon potential at the levels $(1/2,\,1)$ and $(2,\,6)$. "$-1$" is equal to the minus tension of non BPS D$p$-brane $\tilde{\tau}_p=\frac{2}{\pi^2 g^2_o\alpha^{\,\prime\,\frac{p+1}{2}}}$.