On Branches of Numerical “Double Brane” Solution in Open String Field Theory Around the Identity-Based Solution

The Takahashi-Tanimoto identity-based solution in bosonic open string field theory contains one real parameter a. From various viewpoints, it has been confirmed that the solution is pure-gauge for a> -1/2 and represents the tachyon vacuum for a= -1/2. In particular, we have obtained a consistent numerical result with the above for the "double brane" solution in the previous work using the level truncation approximation. In the literature, we obtained the "double brane" solution in theory around the identity-based solution as follows: firstly, we constructed the "double brane" solution for various values of a at truncation level two, and then we constructed numerical solutions at each a level by level. Alternatively, at each truncation level, we can construct numerical solutions from Kudrna-Schnabl's "double brane" solution, which corresponds to the case a =O, by varying the value of a little by little. We have found that solutions by two methods are in different branches for a region of a at truncation levels 20 and 22. Here, we plot gauge invariants for them and give some comments on consistency.