On the Effective Field Theory of Heterotic Vacua

TL;DR

This paper advances the understanding of heterotic string vacua by computing key couplings in the effective field theory, including the Kahler potential and superpotential, to first order in alpha prime, for vacua with specific geometric properties.

Contribution

It provides explicit calculations of matter sector contributions, Yukawa couplings, and fermionic couplings in the effective theory of heterotic vacua, extending previous work on moduli metrics.

Findings

Derived the Kahler potential and superpotential for heterotic vacua.

Calculated matter sector contributions to the Kahler potential.

Determined Yukawa and quadratic fermionic couplings.

Abstract

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 $\mathcal{W}$ .