Abstract
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.
Highlights
Open bosonic string field theories on a D-brane have a stable vacuum where a tachyon field is condensed and the D-brane disappears
We have studied sine-square-like deformation (SSLD) in open string systems and clarified that the left and right moving modes in the SSLD system are decoupled and uncorrelated by zeros of the weighting function of the Hamiltonian
We considered open string field theory (SFT) expanded around the identity-based tachyon vacuum solution
Summary
Open bosonic string field theories on a D-brane have a stable vacuum where a tachyon field is condensed and the D-brane disappears. They found that this system is equivalent to a system with a periodic boundary condition by calculating the ground state energy and correlation functions numerically This result suggests that a discretized closed system can be described by degrees of freedom of a discretized open system, and, considering the continuum limit, the above idea is realized in a 2D field theory. We will obtain holomorphic and antiholomorphic continuous Virasoro operators that commute with the modified BRST operator on the identity-based tachyon vacuum The existence of such Virasoro operators implies that open SFT on the identity-based tachyon vacuum provides some observables given by the worldsheet without boundaries, i.e., observables of closed string theories.
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