Solitons and Yukawa Couplings in Nearly Kahler Flux Compactifications

TL;DR

This paper investigates flux compactifications on a nearly Kahler manifold, deriving scalar potentials, gauge and fermion masses, and identifying soliton solutions, with implications for heterotic string vacua.

Contribution

It introduces a detailed analysis of vacuum structures, scalar potentials, and fermion masses in nearly Kahler flux compactifications, including a sine-Gordon sector and explicit Yukawa interactions.

Findings

Derived scalar potentials and mass spectra as functions of moduli.

Identified a sine-Gordon type integrable subsector with soliton solutions.

Found conditions supporting heterotic flux vacua.

Abstract

We study vacuum states and symmetric fermions in equivariant dimensional reduction of Yang-Mills-Dirac theory over the six-dimensional homogeneous space SU(3)/U(1)x U(1) endowed with a family of SU(3)-structures including a nearly Kahler structure. We derive the fixed tree-level scalar potentials of the induced Yang-Mills-Higgs theory, and compute the dynamically generated gauge and Higgs boson masses as functions of the metric moduli of the coset space. We find an integrable subsector of the Higgs field theory which is governed by a sine-Gordon type model whose topological soliton solutions are determined nonperturbatively by the gauge coupling and which tunnel between families of infinitely degenerate vacua. The reduction of the Dirac action for symmetric fermions yields exactly massless chiral fermions, containing subsectors which have fixed tree-level Yukawa interactions. We compute dynamical fermion mass matrices explicitly and compare them at differents points of the moduli space, some of which support consistent heterotic flux vacua.