On the Effective Field Theory of Heterotic Vacua

The effective field theory of heterotic vacua that realise $\mathbb{R}^{3,1}$ preserving $\mathcal{N} =1$ supersymmetry are studied. The vacua in question admit large radius limits taking the form $\mathbb{R}^{3,1}\times {X}$ , with ${X}$ a smooth three-fold with vanishing first Chern class and a stable holomorphic gauge bundle $\mathcal{E}$. In a previous paper we calculated the kinetic terms for moduli, deducing the moduli metric and Kahler potential. In this paper, we compute the remaining couplings in the effective field theory, correct to first order in alpha prime. In particular, we compute the contribution of the matter sector to the Kahler potential, derive the Yukawa couplings and other quadratic fermionic couplings. From this we write down a Kahler potential $\mathcal{K}$ and superpotential $\mathcal{W}$ .