Super-Yang–Mills, Chern–Simons couplings and their all order $$\alpha '$$ α ′ corrections in IIB superstring theory

Abstract

We explore the closed form of the correlation function of four spin operators (including one closed string Ramond–Ramond (RR) and two open string fermions) and one current in ten dimensions, to be able to find the complete and the closed form of the amplitude of one closed string Ramond–Ramond, one gauge field and two fermionic strings (with the same chirality) to all orders in \(\alpha '\) in IIB superstring theory. In particular we use a special gauge fixing to the amplitude and apply fermions’ equations of motion to \(\langle V_{C} V_{A}V_{\bar{\psi }}V_{\psi }\rangle \) correlator. The string amplitude implicated that neither there should be any \(u\)-channel gauge poles for \(p=n+2\) case nor there are couplings between two fermions and two gauge fields for \(p=n\) case in the field theory of type IIB. All infinite \(u\)-channel scalar poles and \(t,s\)-channel fermion poles of the string amplitude are useful in discovering new couplings of type IIB. More specifically, by making use of the SYM couplings of one scalar, one gauge and two fermions and their all order \(\alpha '\) higher derivative corrections, we are able to exactly produce all infinite \((s+t+u)\)-channel scalar poles of \(\langle V_{C} V_{A}V_{\bar{\psi }}V_{\psi }\rangle \).