Energy from the gauge invariant observables

Abstract

For a classical solution |Ψ〉 in Witten’s cubic string field theory, the gauge invariant observable 〈I|$\mathcal{V}$|Ψ〉 is conjectured to be equal to the difference of the one-point functions of the closed string state corresponding to $\mathcal{V}$, between the trivial vacuum and the one described by |Ψ〉. For a static solution |Ψ〉, if $\mathcal{V}$ is taken to be $c\overline{c}\partial {X^0}\overline{\partial}{X^0}$, the gauge invariant observable is expected to be proportional to the energy of |Ψ〉. We prove this relation assuming that |Ψ〉 satisfies equation of motion and some regularity conditions. We discuss how this relation can be applied to various solutions obtained recently.