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

Erasmo Coletti, Valentina Forini, Giuseppe Nardelli, Gianluca Grignani, Gianluca Luigi Grignani, Marta Orselli, Matteo Orselli

Research output: Contribution to journalArticlepeer-review

Abstract

We compute, on the disk, the non-linear tachyon β-function, βT, of the open bosonic string theory. βT 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 βT. 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. © SISSA/ISAS 2004.
Original languageEnglish
Pages (from-to)683-712
Number of pages30
JournalJournal of High Energy Physics
Volume8
Publication statusPublished - 2004

Keywords

  • Tachyon Condensation
  • String Field Theory

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