Ghost story. I. Wedge states in the oscillator formalism

Details Ghost story. I. Wedge states in the oscillator formalism Ghost story. I. Wedge states in the oscillator formalism

2007-06-07

arxiv.org/abs/0706.1025v3

JHEP 0709:061,2007

Physics

High Energy Physics

High Energy Physics - Theory

53 pages, latex, subsection 2.5 and section 6 enlarged, to appear in JHEP

Scientific paper

10.1088/1126-6708/2007/09/061

This paper is primarily devoted to the ghost wedge states in string field theory formulated with the oscillator formalism. Our aim is to prove, using such formalism, that the wedge states can be expressed as |n> = exp[{2-n}/2 ({\cal L}_0+{\cal L}_0^\daggert)]|0>, separately in the matter and ghost sector. This relation is crucial for instance in the proof of Schnabl's solution. We start from the exponentials in the rhs and wish to prove that they take precisely the form of wedge states. As a guideline we first re-demonstrate this relation for the matter part. Then we turn to the ghosts. On the way we face the problem of `diagonalizing' infinite rectangular matrices. We manage to give a meaning to such an operation and to prove that the eigenvalues we obtain satisfy the recursion relations of the wedge states.

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