On the effective field theory of heterotic vacua

The effective field theory of heterotic vacua that realise [Formula: see text] preserving [Formula: see text] supersymmetry is studied. The vacua in question admit large radius limits taking the form [Formula: see text], with [Formula: see text] a smooth threefold with vanishing first Chern class and a stable holomorphic gauge bundle [Formula: see text]. In a previous paper we calculated the kinetic terms for moduli, deducing the moduli metric and Kähler potential. In this paper, we compute the remaining couplings in the effective field theory, correct to first order in [Formula: see text]. In particular, we compute the contribution of the matter sector to the Kähler potential and derive the Yukawa couplings and other quadratic fermionic couplings. From this we write down a Kähler potential [Formula: see text] and superpotential [Formula: see text].