A simple solution for marginal deformations in open string field theory

Abstract

We derive a new open string field theory solution for boundary marginal deformations generated by chiral currents with singular self-OPE. The solution is algebraically identical to the Kiermaier-Okawa-Soler solution and it is gauge equivalent to the TakahashiTanimoto identity-based solution. It is wedge-based and we can analytically evaluate the Ellwood invariant and the action, reproducing the expected results from BCFT. By studying the isomorphism between the states of the initial and final background a dual derivation of the Ellwood invariant is also obtained.

BCFT moduli space in level truncation

“…Going back to OSFT, the tachyon coefficient of the analytic solution [10] was also shown to asymptote (from above, after a local maximum), to a constant positive value 1 A similar problem, from a complementary different perspective, has been addressed, up to level (3,9), in [22].…”

“…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].…”

“…There is a simple explanation for this: OSFT is a gauge theory and the solution has to come back to itself only up to a (large) gauge transformation, upon winding around the circular moduli space. In particular the OSFT solution describing the translation of a D0-brane does not depend on the compactification radius and the circular moduli space is formed because the boundary condition changing operators translating by 2πR are in fact genuine fields of the theory (they are the open string winding modes) from which it is possible to build the abovementioned gauge transformations, [5,10]. The toy model, on the other hand, does not have any gauge symmetry and the solution has to be strictly periodic in λ B .…”

“…Concrete examples of these 'far' solutions in OSFT have been presented in [10] and in [5] building on [11][12][13][14][15]. It is therefore an important question whether we can find these solutions in Siegel gauge as well.…”

Comments on lump solutions in SFT

“…After the discovery [1,2] of the first analytic solution of open SFT à la Witten [3], which links the perturbative vacuum to the tachyon vacuum, there have been a considerable number of papers devoted to related solutions [4,5] and to marginal deformations thereof [6][7][8][9][10][11][12][13]. The literature concerning analytic lump solutions, i.e.…”