Tachyon potentials, star products and universality

TL;DR

Rastelli and Zwiebach develop a background-independent, recursion-based framework for open bosonic string field theory tachyon condensation by exploiting the universal subspace ${\cal H}_{univ}$ and Virasoro conservation laws. Their approach avoids explicit conformal transformations and background selection, enabling efficient level-truncation calculations, exemplified by a level-(2,6) tachyon potential and explicit velocity of star products, including the identity and wedge-state structures. They establish that ${\cal H}_{univ}$ is a star-algebra substructure and that the identity and wedge states form a coherent, background-independent subalgebra, providing a path toward analytic tachyon condensates. The results advance computational techniques in OSFT, with potential implications for brane dynamics and extensions to superstring field theory.

Abstract

We develop an efficient recursive method to evaluate the tachyon potential using the relevant universal subalgebra of the open string star algebra. This method, using off-shell versions of Virasoro Ward identities, avoids explicit computation of conformal transformations of operators and does not require a choice of background. We illustrate the procedure with a pedagogic computation of the level six tachyon potential in an arbitrary gauge, and the evaluation of a few simple star products. We give a background independent construction of the so-called identity of the star algebra, and show how it fits into family of string fields generating a commutative subalgebra.

Figures (5)

• Figure 1: Representation of the cubic vertex as the gluing of 3 half--disks.
• Figure 2: Representation of the cubic vertex as the gluing of 3 semi--infinite strips.
• Figure 3: The result of gluing the 3 strips of Fig. \ref{['strips']}.
• Figure 4: Representation of the cubic vertex as a 3--punctured unit disk.
• Figure 5: Representation of the cubic vertex as the upper--half plane with 3 punctures on the real axis.