On higher derivative corrections to Wess-Zumino and Tachyonic actions in type II super string theory

TL;DR

This paper computes string scattering amplitudes involving scalars, tachyons, and Ramond-Ramond fields in type II superstring theory, deriving all-order couplings and confirming their consistency with field theory predictions, including higher derivative corrections.

Contribution

It provides the first detailed all-order $\alpha'$ couplings of scalars and tachyons to Ramond-Ramond fields and extends the Wess-Zumino action to incorporate these new interactions.

Findings

Confirmed infinite tachyon poles match field theory predictions.

Derived all-order $\alpha'$ couplings for scalars and tachyons.

Extended Wess-Zumino action to include new couplings.

Abstract

We evaluate in detail the string scattering amplitude to compute different interactions of two massless scalars, one tachyon and one closed string Ramond-Ramond field in type II super string theory. In particular we find two scalar field and two tachyon couplings to all orders of $\alpha'$ up to on-shell ambiguity. We then obtain the momentum expansion of this amplitude and apply this infinite number of couplings to actually check that the infinite number of tachyon poles of S-matrix element of this amplitude for the $p=n$ case (where $p$ is the spatial dimension of a D$_p$-brane and $n$ is the rank of a Ramond-Ramond field strength) to all orders of $\alpha'$ is precisely equal to the infinite number of tachyon poles of the field theory. In addition to confirming the couplings of closed string Ramond-Ramond field to the world-volume gauge field and scalar fields including commutators, we also propose an extension of the Wess-Zumino action which naturally reproduces these new couplings in field theory such that they could be confirmed with direct S-matrix computations. Finally we show that the infinite number of massless poles and contact terms of this amplitude for the $p=n+1$ case can be reproduced by Chern-Simons, higher derivative corrections of the Wess-Zumino and symmetrized trace tachyon DBI actions.