All order $\alpha'$ higher derivative corrections to non-BPS branes of type IIB Super string theory

TL;DR

This paper derives the complete set of all-order higher derivative corrections to the interactions of non-BPS branes in type IIB superstring theory by analyzing specific string amplitudes involving fermions, tachyons, and Ramond-Ramond fields.

Contribution

It provides the first explicit all-order higher derivative corrections to two tachyons and two fermions in type IIB superstring theory, matching string amplitudes with effective field theory.

Findings

All-order higher derivative corrections for two tachyons and two fermions are obtained.

Infinite tachyon poles in string theory are reproduced in field theory using new couplings.

No coupling exists between two RR fields and a single tachyon in type II superstring theory.

Abstract

By dealing with the evaluation of string theory correlators of $<V_C V_T V_{\bar\Psi} V_\Psi>$, the complete and closed form of the amplitude of two fermion fields, one tachyon and one closed string Ramond-Ramond field in type IIB superstring theory is found. Specifically by comparing infinite tachyon poles in field theory amplitude with infinite tachyon poles of the S-matrix of string amplitude (for $p+1=n$ case), all the infinite higher derivative corrections of two tachyons and two fermions (in type IIB) to all orders of $\alpha'$ have been discovered. Using these new couplings, we are able to produce infinite $t'+s'+u$-channel tachyon poles of string theory in field theory. Due to internal degrees of freedom of fermions and tachyon (Chan-Paton factors) we comment that, neither there should be single $s,t-$channel fermion (tachyon pole) nor their infinite poles. Due to internal CP factor we also discover that there is no coupling between two closed string Ramond-Ramond (RR) field and one tachyon in type II super string theory. Taking into account the fact that the kinetic terms of fermions, gauge, scalar fields and tachyons do not obtain any higher derivative corrections, and due to their CP factors, string theory amplitude dictates us there should not be any double poles in the amplitude of one RR, two fermions and one tachyon.