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.

22 pages, 4 figures, published version

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Cited by in corpus (1)

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