Exact potential and scattering amplitudes from the tachyon non-linear $β$-function

Details Exact potential and scattering amplitudes from the tachyon non-linear $β$-function Exact potential and scattering amplitudes from the tachyon non-linear $β$-function

2004-02-22

arxiv.org/abs/hep-th/0402167v1

JHEP 0403:030,2004

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 1 figure, JHEP3.cls

Scientific paper

10.1088/1126-6708/2004/03/030

We compute, on the disk, the non-linear tachyon $\beta$-function, $\beta^T$, of the open bosonic string theory. $\beta^T$ is determined both in an expansion to the third power of the field and to all orders in derivatives and in an expansion to any power of the tachyon field in the leading order in derivatives. We construct the Witten-Shatashvili (WS) space-time effective action $S$ and prove that it has a very simple universal form in terms of the renormalized tachyon field and $\beta^T$. The expression for $S$ is well suited to studying both processes that are far off-shell, such as tachyon condensation, and close to the mass-shell, such as perturbative on-shell amplitudes. We evaluate $S$ in a small derivative expansion, providing the exact tachyon potential. The normalization of $S$ is fixed by requiring that the field redefinition that maps $S$ into the tachyon effective action derived from the cubic string field theory is regular on-shell. The normalization factor is in precise agreement with the one required for verifying all the conjectures on tachyon condensation. The coordinates in the space of couplings in which the tachyon $\beta$-function is non linear are the most appropriate to study RG fixed points that can be interpreted as solitons of $S$, $i.e.$ D-branes.

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