By Ohmori, K
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Additional info for A Review on Tachyon Condensation in Open String Field Theories
If the kinetic term of a massive field vanishes at the nonperturbative vacuum, its mass effectively grows to infinity and the field decouples from the spectrum there. This decoupling mechanism nicely fits the conjecture of annihilation of the Dbrane. e. two derivatives) kinetic term of the gauge field is shown to be absent at the nonperturbative vacuum, as long as the conjecture f (T0 ) = −1 is true. Its outline is as follows. Under this assumption, one can show that the value of the potential at T = T0 is independent of the classical background of the massless fields on the original D-brane (T = 0), if it is a classical solution to the equations of motion at T = 0.
In contrast, the new vacuum found in the previous sections, where various fields develop nonzero expectation values, is termed ‘nonperturbative vacuum’ for reasons discussed below, or ‘closed string vacuum’ because we believe that in this new vacuum the negative energy contribution from the tachyon potential associated with the rolling down of the tachyon field exactly cancels the positive energy density (tension) of the D-brane, resulting in a true vacuum without any D-brane or open string. Here a problem can arise: On a single bosonic D-brane, the tachyon field is in the adjoint representation and hence is neutral under the U(1) gauge group.
This means that if we restrict the transformations to SL(2, C) ones, we cz + d can tentatively regard T (z) as a true tensor field. Then the integrand transforms as a weight 0 primary, v(z)T (z)dz = v ′ (z ′ )T ′ (z ′ )dz ′ ; if z ≡ z ′ mod SL(2, C). 77) and regularity at infinity. 17) as V3 | C v(z)T (z)dz|Φ 1 ⊗ |Φ 2 ⊗ |Φ 3 = 0. 78) does not depend on any properties of Φ at all. Next we deform the contour C to three small circles Ci each of which encircles the insertion point fi (0). At the same time, we perform the conformal transformation from global coordinate z to local coordinate zi associated with three string world-sheets.
A Review on Tachyon Condensation in Open String Field Theories by Ohmori, K