The classical solutions with $k_-=0$ in Kaku theory

TL;DR

This paper shows that classical solutions with a specific restriction in Kaku string field theory are equivalent to those in Witten theory, confirming the trivial cohomology around the tachyon vacuum in Kaku theory.

Contribution

It demonstrates the equivalence of certain classical solutions between Kaku and Witten theories and confirms the trivial cohomology in Kaku theory around the tachyon vacuum.

Findings

Solutions with $k_-=0$ satisfy Witten theory equations

Tachyon vacuum solutions are shared between theories

Cohomology around tachyon vacuum is trivial in Kaku theory

Abstract

We consider Kaku theory as introduced in M. Kaku, Phys. Lett. B 200, 22 (1988) and investigate classical solutions. In particular, we obtain that the equation of motion with the restriction $k_-=0$ in the Kaku theory is equivalent to the equation of motion in Witten theory. Because of this property, some solutions including the tachyon vacuum solution in the Witten theory satisfy also the equation of motion in the Kaku theory. In addition, we confirm that the cohomology around the tachyon vacuum solution is trivial also in the Kaku theory.