Numerical hermitian yang-Mills connection for bundles on quotient manifold

We extend previous computations of Hermitian Yang–Mills connections for bundles on complete intersection Calabi–Yau manifolds to bundles on their free quotients. Bundles on quotient manifolds are often defined by equivariant bundles on corresponding covering spaces. Combining equivariant structure and the generalized Donaldson algorithm, we develop a systematic approach to compute connections of holomorphic poly-stable bundles on quotient manifolds. With it, we construct connections of an SU(3) bundle on a Z 5 quotient of the quintic and an SU(5) bundle on a Z 3 × Z 3 quotient of the bi-cubic. For both examples, the algorithm converges as expected and gives a good approximation of Hermitian Yang–Mills connections, which will be important for heterotic model building in Calabi–Yau compactifications.