Energy from the gauge invariant observables

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.

27 pages; v5: minor revision in section 2, results unchanged

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• Rolling tachyon and the Phase Space of Open String Field Theory
• Gauge Invariant Overlaps for Identity-Based Marginal Solutions
• On Nontrivial Solutions around a Marginal Solution in Cubic Superstring Field Theory
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• Level Truncation Approach to Open String Field Theory
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• $KBc$ algebra and the gauge invariant overlap in open string field theory
• Singular field redefinition between Witten's string field theory and Witten's theory deformed by Ellwood invariant
• Winding number for arbitrary integer value in Cubic String Field Theory