By Ohmori, K
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Extra info for A Review on Tachyon Condensation in Open String Field Theories
2 13 Here we make a comment on the level truncation. In the level (M, N) truncation, in order for the quadratic terms (kinetic term + mass term) for the level M fields to be included in the action, N must be equal to or larger than 2M. On the other hand, as we are using the cubic string field theory action, N cannot become larger than 3M. So the possible truncation levels are (M, 2M) ∼ (M, 3M). 63), where the superscripts (4),(6) indicates the truncation level. Though we do not repeat them here, the expressions for the potential both at level (2,4) and at (2,6) are shown in .
65), f (φ) = 2π 2 α′3 − 1 where κ ≡ 3! 3659 . 456 1 ≃ . 456/α′go . This expression suggests the nonperturbative nature of the ‘closed string vacuum’. 98) to reconcile the definition of κ here with that of  and . 97). Since the potential is quadratic both in β1 and in v, we can eliminate these two fields by integrating them out exactly. The resulting effective tachyon potential is, in the α′ = 1 unit, given by feff (φ) = √ 256 288 + 581 3 φ 6π 2 φ2 √ 2 432 + 786 3 φ + 97 φ2 √ × −660451885056 − 4510794645504 3 φ √ − 32068942626816 φ2 − 25455338339328 3 φ3 + 27487773823968 φ4 √ √ + 54206857131636 3 φ5 + 24845285906980 φ6 + 764722504035 3 φ7 .
Since to H11 , and by S(T 1 1 the fields in H1 have zero momenta and hence are independent of the coordinates on the D-brane world-volume, the integration over x gives the (p + 1)-dimensional volume factor Vp+1 . 53) where we defined the tachyon potential U(T ) as the negative of the Lagrangian. By definition of H11 , the truncated action S˜ is entirely given by the correlation functions involving only the ghost fields b, c and matter energy momentum tensor T m . In the oscillator representation, we only need the commutation relations among bn , cn and the matter Virasoro algebra.