Level Four Approximation to the Tachyon Potential in Superstring Field Theory

TL;DR

This work tests Sen's tachyon vacuum conjecture within Berkovits' NS-sector superstring field theory by performing a level-truncation calculation up to level $4$, including fields up to level $2$. The tachyon potential is computed via conformal field theory correlators (aided by Mathematica) and decomposed into contributions $V_0$, $V_{3/2}$, $V_2$, $V_3$, $V_{7/2}$, and $V_4$, yielding an extremum at which $V = -0.891287\,M$, i.e. $89\%$ of the conjectured value $-M$. The results corroborate gradual convergence toward the conjectured vacuum energy and demonstrate the method's viability, albeit with slower convergence than in prior levels. The authors propose extending to higher levels and studying massless vector interactions to compare with non-Abelian DBI proposals and deepen understanding of level-truncation in superstring field theory.

Abstract

We compute the tachyon potential to level 4 in NS superstring field theory. We obtain 89% of the conjectured vacuum energy.