The Off-Shell Boundary State and Cross-Caps in the Genus Expansion of String Theory

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We use the boundary state formalism for the bosonic string to calculate the emission amplitude for closed string states from particular D-branes. We show that the amplitudes obtained are exactly the same as those obtained from the world-sheet sigma model calculation, and that the construction enforces the requirement for integrated vertex operators, even in the off-shell case. Using the expressions obtained for the boundary state we propose higher order terms in the string loop expansion for the background considered.
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