UV Finite Brane Decay

TL;DR

The paper investigates brane decay in subcritical string theory with a spacelike linear dilaton, addressing the tachyon dust puzzle by computing the full annulus partition function and its imaginary part, which encodes $Im Z$ for closed-string emission. It shows that UV divergences are removed for $D<26$ when the dilaton is spacelike, and it analyzes open-string pair production in the same background, demonstrating finiteness and regulator behavior. The work provides a framework for reconciling time-dependent backgrounds with consistent worldsheet CFTs, clarifying vacuum ambiguities in the annulus and offering insights into energy transfer between branes, open strings, and closed strings. These results have implications for the tachyon dust interpretation and for understanding time-dependent backgrounds in subcritical string theory.

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.

Figures (3)

• Figure 1: Brane decay in the frame in which the dilaton is time-independent but grows with $\tilde{x}^1$. In this frame, the tachyon dust produced by a normalizable decay mode drifts towards weak coupling with constant velocity. Both the energy density of the dust and the energy density of the brane which produced it decrease exponentially towards the strong coupling region.
• Figure 2: In the unbounded from below potential V(t), there are two kinds of eigenstates. Those with positive total energy oscillate in the far past, and correspond to on-shell strings propagating on the brane. Those with negative energy decay exponentially in the far past and are always off-shell. Poles in the spectral density of these unphysical states correspond to closed string emission.
• Figure 3: The annulus can be interpreted as the square of a closed string one-point function or open string two point function, depending on how it is sliced. Corresponding imaginary parts from on-shell closed string emission or open string pair production can appear in different kinematical regions of the diagram.