Universality in all-order ${\alpha }^{\prime }$ corrections to BPS/non-BPS brane world volume theories

Abstract

Knowledge of all-${\alpha }^{\prime }$ higher derivative corrections to leading order BPS and non-BPS brane actions would serve in future endeavor of determining the complete form of the non-abelian BPS and tachyonic effective actions. In this paper, we note that there is a universality in the all-${\alpha }^{\prime }$ order corrections to BPS and non-BPS branes. We compute amplitudes between one Ramond-Ramond $C$-field vertex operator and several SYM gauge/scalar vertex operators. Specifically, we evaluate in closed form string correlators of two-point amplitudes ${\mathcal{A}}^{\mathcal{C}\varphi }$, ${\mathcal{A}}^{\mathcal{C}\mathcal{A}}$, a three-point amplitude ${\mathcal{A}}^{\mathcal{C}\varphi \varphi }$ and a four-point amplitude ${\mathcal{A}}^{\mathcal{C}\varphi \varphi \varphi }$. We carry out pole and contact term analysis. In particular we reproduce some of the contact terms and the infinite massless poles of ${\mathcal{A}}^{\mathcal{C}\varphi \varphi \varphi }$ by SYM vertices obtained through the universality.

arXiv comment29 pages, 4figures, Refs and some applications for higher derivative corrections have been added. Version to appear in NPB

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