Tachyon potentials, star products and universality

TL;DR

The paper introduces a recursive method to evaluate tachyon potentials in open string field theory, leveraging universal subalgebras and off-shell Ward identities, avoiding complex conformal transformations and background dependence.

Contribution

It presents a novel recursive approach for computing tachyon potentials using universal subalgebras and off-shell Ward identities, simplifying calculations in string field theory.

Findings

Efficient recursive method for tachyon potential evaluation

Background independent construction of star algebra identity

Explicit computation of level six tachyon potential

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.