R ⁴ , purified

Abstract

We derive, using the pure-spinor formalism, the complete -including the fermions -fourpoint effective action of both type II superstrings to all orders in α ′ , at tree level in string loops. We find that, in the quartic-field approximation, the supergravity Lagrangian can be thought of as the tensor product, in a suitable sense, of two copies of the superYang-Mills Lagrangian in ten dimensions. The NS-NS three-form enters the supergravity Lagrangian through a modified connection with torsion. As a byproduct, we derive the complete, i.e. to all orders in the θ-expansion, closed-string vertex operator in a flat target-space background.

Duality groups, automorphic forms, and higher derivative corrections

“…Rather one finds that the various vectors that arise are elements of the weight lattice of E 8 . Moreover one only finds weights for the types of higher derivative terms that are expected to arise in M-theory [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Weights have also appeared in the higher derivative effective action in [58,59] within the context of E 10 and 'cosmological billiards' [60,61].…”

Two Ramond–Ramond corrections to type II supergravity via field-theory amplitude

“…Each of these approaches has been employed in different formalisms such as the RNS (Ramond-Neveu-Schwarz) [22][23][24], GS (Green-Schwarz) [17,20,26,27] and pure-spinor [28] formalisms to determine the higher-order terms.…”

Theta expansion of first massive vertex operator in pure spinor

“…This typically requires some gauge fixing and the knowledge of algebraic and differential relations 1 between the superfields. The θ expansion for the massless vertex operator was done in [23][24][25].…”