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

Coletti, E., Forini, V., Nardelli, G., Grignani, G. & Orselli, M. (2004). Exact potential and scattering amplitudes from the tachyon non-linear β-function. Journal of High Energy Physics, 2004, 030.. doi: 10.1088/1126-6708/2004/03/030

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We compute, on the disk, the non-linear tachyon β-function, β T , of the open bosonic string theory. β 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 β 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 β-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.

Item Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8113/48/8/085401.
Uncontrolled Keywords: Tachyon Condensation, String Field Theory
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/19747

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