Energy from the gauge invariant observables

Abstract

For a classical solution |Ψ〉 in Witten's cubic string field theory, the gauge invariant observable 〈I| (V) |Ψ〉 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 |Ψ〉. For a static solution |Ψ〉, if (V) is taken to be cc∂X0∂X0, 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. © 2013 SISSA, Trieste, Italy.