Energy from the gauge invariant observables

TL;DR

The paper proves that for classical solutions in Witten's cubic string field theory, gauge invariant observables relate directly to the energy of the solution, confirming a key conjecture in the field.

Contribution

It provides a proof of the relation between gauge invariant observables and energy for static solutions in string field theory under certain conditions.

Findings

Gauge invariant observable equals the energy for static solutions.

The relation holds assuming the solution satisfies equations of motion and regularity.

Discusses applications to recent solutions in string field theory.

Abstract

For a classical solution |Psi> in Witten's cubic string field theory, the gauge invariant observable <I|V|Psi> is conjectured to be equal to the difference of the one-point functions of the closed string state corresponding to V, between the trivial vacuum and the one described by |Psi>. For a static solution |Psi>, if V is taken to be the graviton vertex operator with vanishing momentum, the gauge invariant observable is expected to be proportional to the energy of |Psi>. We prove this relation assuming that |Psi> satisfies equation of motion and some regularity conditions. We discuss how this relation can be applied to various solutions obtained recently.