Problems for (2, 0) compactifications

Several theoretical and phenomenological problems are exposed which impede the construction of realistic low-energy-models based on the superstring using manifolds for which the gauge and spin connections are not identified (A≠ω), and the world-sheet σ-model has (2, 0) supersymmetry. Single world-sheet instantons generate an effective scalar potential which prevents generic manifolds of this type from being solutions to the equations of motion. They also give large supersymmetry-breaking mass parameters O(m_P) to gauge non-singlet fields. The Green-Schwarz modification to the antisymmetric tensor field strength may not absorb anomalies if ω≠A. It is difficult to obtain satisfactory mixing among the supersymmetric Weinberg-Salam Higgs fields, which requires an SU(3)×SU(2)×U(1) singlet field N with vacuum expectation value x≡〈0{divides}N{divides}0〉=O(m_w). A Yukawa coupling λN³ would yield x=O(m_w), but at the expense of cosmologically unacceptable domain walls. If there is no such Yukawa coupling, the natural value for x is O(m_P).