Comments on Heterotic Flux Compactifications

الأصل · EN

In heterotic flux compactification with supersymmetry, three different connections with torsion appear naturally, all in the form ω+a H. Supersymmetry condition carries a=-1, the Dirac operator has a=-1/3, and higher order term in the effective action involves a=1. With a view toward the gauge sector, we explore the geometry with such torsions. After reviewing the supersymmetry constraints and finding a relation between the scalar curvature and the flux, we derive the squared form of the zero mode equations for gauge fermions. With H=0, the operator has a positive potential term, and the mass of the unbroken gauge sector appears formally positive definite. However, this apparent contradiction is avoided by a no-go theorem that the compactification with H≠ 0 and H=0 is necessarily singular, and the formal positivity is invalid. With H≠ 0, smooth compactification becomes possible. We show that, at least near smooth supersymmetric solution, the size of H² should be comparable to that of H and the consistent truncation of action has to keep α'R² term. A warp factor equation of motion is rewritten with α' R² contribution included precisely, and some limits are considered.