Some exact computations on the twisted butterfly state in string field theory

The twisted butterfly state solves the equation of motion of vacuum stringfield theory in the singular limit. The finiteness of the energy density of thesolution is an important issue, but possible conformal anomaly resulting fromthe twisting has prevented us from addressing this problem. We present adescription of the twisted regulated butterfly state in terms of a conformalfield theory with a vanishing central charge which consists of the ordinary bcghosts and a matter system with c=26. Various quantities relevant to vacuumstring field theory are computed exactly using this description. We find thatthe energy density of the solution can be finite in the limit, but thefiniteness depends on the subleading structure of vacuum string field theory.We further argue, contrary to our previous expectation, that contributions fromsubleading terms in the kinetic term to the energy density can be of the sameorder as the contribution from the leading term which consists of the midpointghost insertion.Comment: 36 pages, no figures, LaTeX2e; v2: minor corrections; v3: typos corrected, published in JHEP; v4: a minor typo in (C.12) correcte