Decay Modes of Unstable Strings in Plane-Wave String Field Theory

Abstract

The cubic interaction vertex of light-cone string field theory in the plane-wave background has a simple effective form when considering states with only bosonic excitations. This simple effective interaction vertex is used in this paper to calculate the three string interaction matrix elements for states of arbitrary bosonic excitation and these results are used to examine certain decay modes on the mass-shell. It is shown that the matrix elements of one string to two string decays involving only bosonic excitations will vanish to all orders in 1/mu on the mass-shell when the number of excitations on the initial string is less than or equal to two, but in general will not vanish when the number of excitations is greater than two. Also, a truncated calculation of the mass-shell matrix elements for one string to three string decays of two excitation states is performed and suggests that these matrix elements do not vanish on the mass-shell. There is, however, a quantitative discrepancy between this last result and its (also non-vanishing) gauge theory prediction from the BMN correspondence.

11 pages; v2: references added; v3: normalization of interaction vertex and corresponding amplitudes changed by a factor of mu to reflect SFT normalization (must now divide by mu to compare with BMN dual gauge theory), and minor errors corrected

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Cited by in corpus (3)

• New aspects of the BMN correspondence beyond the planar limit
• Decay widths of three-impurity states in the BMN correspondence
• Four-Impurity Operators and String Field Theory Vertex in the BMN Correspondence