# All Order $\alpha'$ Corrections to Fermionic Couplings of D-brane-Anti-D-brane Effective Actions

## TL;DR

This paper derives all order $\alpha'$ corrections to fermionic couplings in D-brane Anti-D-brane systems in type II superstring theory, revealing new string couplings and singularity structures through CFT and EFT methods.

## Contribution

It provides the first comprehensive all order $\alpha'$ corrections to fermionic couplings and their effective actions for D-brane Anti-D-brane systems, including new couplings and singularity structures.

## Key findings

- All order $\alpha'$ corrections to fermionic couplings are derived.
- New string couplings are identified.
- All order singularity structures of the amplitude are revealed.

## Abstract

We first point out to all order $\alpha'$ corrections to lower order fermionic couplings and their effective actions of type II super string theory. In order to reveal all symmetries of the particular D-brane Anti-D-brane system, and to construct not only all the singularity structures but also all order $\alpha'$ corrections of fermionic couplings to tachyons, we employ all the Conformal Field Theory (CFT) methods to a six point function. Basically, we construct all the correlation functions of four spin operators and two world sheet fermion fields. The S-matrix of two fermion fields, two real tachyons in the presence of a closed string Ramond-Ramond (RR) field in type II will be explored. Applying all the symmetries of the amplitude, a proper expansion for D-brane Anti D-brane is also found out. Having carried out all the Effective Field Theory (EFT) techniques, one would discover all order singularity structures of string theory. The entire algebraic computations of the amplitude of $<V_{C^{-1}(z,\bar z)} V_{\bar\psi^{-1/2}(x_1)} V_{\psi^{-1/2}(x_2)} V_{T^{0}(x_3)} V_{T^{0}(x_4)}>$ have also been derived. Various new string couplings are revealed as well. Eventually, making comparison the S-matrix with all EFT parts, all order $\alpha'$ higher derivative corrections to two fermions -- two tachyons in the world volume of D-brane Anti D-brane of type II are discovered accordingly.