Closed Superstring Emission from Rolling Tachyon Backgrounds

We compute the lowest components of the Type II Ramond-Ramond boundary statefor the tachyon profile $T (X) = \lambda e ^{X ^ 0/\sqrt{2}}$ by direct pathintegral evaluation. The calculation is made possible by noting that theintegrals involved in the requisite disk one-point functions reduce tointegrals over the product group manifold $U (n)\times U (m)$. We further notethat one-point functions of more general closed string operators in thisbackground can also be related to $U (n)\times U (m)$ group integrals. Usingthis boundary state, we compute the closed string emission from a decayingunstable D$p$-brane of Type II string theory. We also discuss closed stringemission from the tachyon profile $T (X) =\lambda\cosh (X ^ 0/\sqrt{2})$. Wefind in both cases that the total number of particles produced diverges for $p= 0$, while the energy radiated into closed string modes diverges for $p\leq2$, in precise analogy to the bosonic case.Comment: 23 page