Abstract
The decay of an unstable D-brane via closed string emission and open string pair production is considered in subcritical string theory with a spacelike linear dilaton. The decay rate is given by the imaginary part of the annulus, which has ambiguities corresponding to the choices of incoming closed and open string vacua. An exact expression for the full annulus diagram is computed with a natural choice of incoming vacua. It is found that the ultraviolet divergences present in critical string theory in both of these processes are absent for any nonzero spacelike dilaton. Implications for the vexing issue of the tachyon dust are discussed.
Highlights
The main result of this paper, on which the preceding statements are based, is the expression for the worldsheet partition function for unstable for p-brane decay in D ≤ 26dimensional string theory
Interpreting the imaginary part as due to closed string emission, this agrees with the result of [13] for closed string emission during brane decay, and generalizes it to the case of a linear dilaton
We show that for D < 26 this divergence is eliminated. Though this divergence is gone in all the different decay channels which we have considered, it is possible that there exist other decay channels where the emission rate diverges again
Summary
We discuss the physics of free strings in the linear dilaton background [22]. Consider string theory in flat space with a linear dilaton Φ = VμXμ. For nonzero V , D must be adjusted to maintain c = 26.5 The mass-shell conditions for closed strings are. On-shell momenta have an imaginary component, −iVμ. This is natural when one examines, for example, the lagrangian for a closed string mode of mass m2 = 2(N + N − 2) in this background. We can refer to φ as the string frame field. The dressing is necessary to make the physical field normalizable with respect to the norm given by the action.
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