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We investigate numerical solutions of bosonic open string field theory insome marginally deformed backgrounds, which are obtained by expanding theaction around an identity-based marginal solution with one parameter. Weconstruct numerical solutions in the Siegel gauge and the Landau gaugecorresponding to the tachyon vacuum. Their vacuum energy approximately cancelsthe D-brane tension for larger intervals of the parameter with increasingtruncation level. The result is consistent with the previous expectation thatthe identity-based marginal solution has vanishing energy regardless of thevalues of the parameter. We also study the marginal branch (M-branch) and thevacuum branch (V-branch) and evaluate not only the vacuum energy but also thegauge invariant overlaps with the graviton and the closed tachyon. We observethat there is a finite bound for the value of the massless field of numericalsolutions even in the marginally deformed background.

Numerical Solutions of Open String Field Theory in Marginally Deformed Backgrounds