On the Witten Rigidity Theorem for Stringc^c Manifolds

We establish the family rigidity and vanishing theorems on the equivariant $K$-theory level for the Witten type operators on String$^c$ manifolds introduced by Chen-Han-Zhang.Comment: arXiv admin note: substantial text overlap with arXiv:1104.3972, and with arXiv:math/0001014, arXiv:math/9912108 by other author

Massive Domain Wall Fermions on Four-dimensional Anisotropic Lattices

We formulate the massive domain wall fermions on anisotropic lattices. For the massive domain wall fermion, we find that the dispersion relation assumes the usual form in the low momentum region when the bare parameters are properly tuned. The quark self-energy and the quark field renormalization constants are calculated to one-loop in bare lattice perturbation theory. For light domain wall fermions, we verified that the chiral mode is stable against quantum fluctuations on anisotropic lattices. This calculation serves as a guidance for the tuning of the parameters in the quark action in future numerical simulations.Comment: 36 pages, 14 figures, references adde