QUANTUM SYMMETRIES AND STRINGY INSTANTONS

The quantum symmetry of many Landau-Ginzburg orbifolds appears to be b roken by Yang-Mills instantons. However, isolated Yang-Mills instanton s are not solutions of string theory: They must be accompanied by gaug e anti-instantons, gravitational instantons, or topologically non-triv ial configurations of the H field. We check that the configurations pe rmitted in string theory do in fact preserve the quantum symmetry, as a result of non-trivial cancellations between symmetry breaking effect s due to the various types of instantons. These cancellations indicate new constraints on Landau-Ginzburg orbifold spectra and require that the dilation modulus mix with the twisted moduli in some Landau-Ginzbu rg compactifications. We point out that one can find similar constrain ts at all fixed points of the modular group of the moduli space of vac ua.