Twisted superspace on a lattice. (English) Zbl 1160.81464
Summary: We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of \(N=2\) twisted supersymmetry invariant BF and Wess-Zumino models in two dimensions. We introduce mild lattice non-commutativity to preserve Leibniz rule on the lattice. The formulation is based on the twisted superspace formalism for \(N=D=2\) supersymmetry which was proposed recently. From the consistency condition of the non-commutativity of superspace, we find an unexpected three-dimensional lattice structure which may reduce into two-dimensional lattice where the superspace describes semilocally scattered fermions and bosons within a double size square lattice.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T25 | Quantum field theory on lattices |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
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