Large BCFT moduli in open string field theory

Abstract

Abstract:We use the recently constructed solution for marginal deformations by one of the authors, to analytically relate the BCFT modulus (λ BCFT ) to the coefficient of the boundary marginal field in the solution (λ SFT ). We explicitly find that the relation is not one to one and the same value of λ SFT corresponds to a pair of different λ BCFT 's: a "small" one, and a "large" one. The BCFT moduli space is fully covered, but the coefficient of the marginal field in the solution is not a good global coordinate on such a space.

BCFT moduli space in level truncation

“…The situation here is more similar to the marginal approach [21]. This suggests that also the tachyon VEV could have a maximum as a function of λ B , as it happens in the analytic example [23] Table 2. The endpoint of the marginal branch in the tachyon approach with 3 digit precision.…”

“…It should be noticed that the behavior for large λ B > πR is sensibly different from the available OSFT example of [23] (see figure 2 and 3 there). On the other hand the plot for λ B < πR is in qualitative agreement with OSFT.…”

“…1 A major common point of these works is that, by parametrizing the marginal solutions with the VEV of the marginal field λ SFT ≡ λ S , no solution can be found after a certain critical value of the BCFT parameter λ BCFT ≡ λ B which, in the case of the cosine deformation of a free boson at the self-dual radius, is close to the point where the initial Neumann boundary condition becomes Dirichlet, [21]. 2 Recently it has been shown in [23] that in the case of the physically equivalent analytic solution [10], which is directly expressed in terms of the BCFT modulus λ B , a power series in λ S would necessarily stop converging at finite radius, simply because λ S is not an injective function of λ B and therefore the dependence on λ S is multi-valued. In particular if we express λ S as a function of λ B we find that it starts growing up to a maximal value and then decreases to zero at large λ B , see figure 2 of [23].…”

“…2 Recently it has been shown in [23] that in the case of the physically equivalent analytic solution [10], which is directly expressed in terms of the BCFT modulus λ B , a power series in λ S would necessarily stop converging at finite radius, simply because λ S is not an injective function of λ B and therefore the dependence on λ S is multi-valued. In particular if we express λ S as a function of λ B we find that it starts growing up to a maximal value and then decreases to zero at large λ B , see figure 2 of [23].…”

BCFT and OSFT moduli: an exact perturbative comparison

“…Conveniently, this solution is directly expressed in terms of the deformation parameter of the underlying BCFT, λ. In [19] this has been used to explicitly find the relation between the BCFT modulus λ and the coefficient of the marginal field in the solution c∂cj| (λ) . It has been observed that this function of λ starts linearly; then it has a local maximum, and finally it approaches zero for large values of λ. Nontrivial evidence that this behavior may also be present in Siegel gauge 3 has been given in [20] in level truncation, but it has not been possible there to establish the validity of the full equations of motion for large BCFT moduli.…”