Effective Tachyonic Potential in Closed String Field Theory

TL;DR

This paper computes the effective tachyonic potential in closed string field theory up to the quartic term, revealing that higher-order corrections eliminate the local minimum found at third order.

Contribution

It provides a detailed calculation of the quartic tachyon potential in closed string field theory, including the effects of an infinite sum over Feynman graphs and the elementary vertex.

Findings

Both elementary and summed contributions are negative.

The quartic term is large enough to remove the local minimum.

Numerical results show the potential's shape changes at fourth order.

Abstract

We calculate the effective tachyonic potential in closed string field theory up to the quartic term in the tree approximation. This involves an elementary four-tachyon vertex and a sum over the infinite number of Feynman graphs with an intermediate massive state. We show that both the elementary term and the sum can be evaluated as integrals of some measure over different regions in the moduli space of four-punctured spheres. We show that both elementary and effective coupling give negative contributions to the quartic term in the tachyon potential. Numerical calculations show that the fourth order term is big enough to destroy a local minimum which exists in the third order approximation.