  We revisit the identity-based solutions for tachyon condensation in open
bosonic string field theory (SFT) from the viewpoint of the sine-square
deformation (SSD). The string Hamiltonian derived from the simplest solution
includes the sine-square factor, which is the same as that of an open system
with SSD in the context of condensed matter physics. We show that the open
string system with SSD or its generalization exhibits decoupling of the left
and right moving modes and so it behaves like a system with a periodic boundary
condition. With a method developed by Ishibashi and Tada, we construct pairs of
Virasoro generators in this system, which represent symmetries for a closed
string system. Moreover, we find that the modified BRST operator in the open
SFT at the identity-based tachyon vacuum decomposes to holomorphic and
antiholomorphic parts, and these reflect closed string symmetries in the open
SFT. On the basis of SSD and these decomposed operators, we construct
holomorphic and antiholomorphic continuous Virasoro algebras at the tachyon
vacuum. These results imply that it is possible to formulate a pure closed
string theory in terms of the open SFT at the identity-based tachyon vacuum.
