Energy from Ellwood invariant for solutions involving $X^0$ variables

Abstract

For some classical solutions ${\Psi }_{\mathrm{sol}}$ in Witten's bosonic string field theory, it was proven that energy of the solution is proportional to the Ellwood invariant $\mathrm{Tr}(\mathcal{V}{\Psi }_{\mathrm{sol}})$ with $\mathcal{V}=c\bar{c}\partial X^0\bar{\partial }{X}^0$. We examine the relation for solutions involving $X^0$ variables. As a result, we obtain that the relation may not hold for such solutions. Namely, there is a possibility that the energy is not proportional to the Ellwood invariant.

arXiv comment22 pages, 4 figures, published version

References in corpus (19)

• Comments on Schnabl's analytic solution for tachyon condensation in Witten's open string field theory
• A Simple Analytic Solution for Tachyon Condensation
• Analytic Solutions for Marginal Deformations in Open String Field Theory
• Comments on Marginal Deformations in Open String Field Theory
• The closed string tadpole in open string field theory
• Analytical Solutions of Open String Field Theory
• String Field Theory Solution for Any Open String Background
• Solutions from boundary condition changing operators in open string field theory
• Relevant Deformations in Open String Field Theory: a Simple Solution for Lumps
• On Multibrane Solutions in Open String Field Theory
• Multibrane Solutions in Open String Field Theory
• Four Lectures on Analytic Solutions in Open String Field Theory
• Energy from the gauge invariant observables
• String Field Theory Solution for Any Open String Background. II
• Constraints on a class of classical solutions in open string field theory
• Inversion Symmetry of Gravitational Coupling in Cubic String Field Theory
• Analytic Construction of Multi-brane Solutions in Cubic String Field Theory for Any Brane Number
• Singular Gauge Transformation and the Erler-Maccaferri Solution in Bosonic Open String Field Theory
• Interior Product, Lie Derivative and Wilson Line in the $KBc$ Subsector of Open String Field Theory

Cited by in corpus (1)

• Singular field redefinition between Witten's string field theory and Witten's theory deformed by Ellwood invariant