Abstract
We prove that the prescription for construction of supersymmetric lattice gauge theories by orbifolding and deconstruction directly leads to Catterall's geometrical discretization scheme in general. These two prescriptions always give the same lattice discretizations when applied to theories of p-form fields. We also show that the geometrical discretization scheme can be applied to more general theories.
Highlights
Among the many recent developments towards putting exactly preserved supersymmetries on a space-time lattice, one of the most striking results is that apparently quite different formulations are related to each other
Catterall has shown that the orbifolded lattice gauge theories for two-dimensional N = (2, 2) SYM theory and four-dimensional N = 4 SYM theory can be derived from topologically twisted continuum theories using the geometrically discretization scheme without additional complexfication of fields [22]
We see that the rules we obtain are precisely those of the geometrical discretization scheme
Summary
Among the many recent developments towards putting exactly preserved supersymmetries on a space-time lattice, one of the most striking results is that apparently quite different formulations are related to each other. 1. The action is Lorentz invariant and consists of complex covariant derivatives Dμ and (bosonic and/or fermionic) tensor fields, {fμ±1···μp}: Scont. The orbifold projection restricts fields in the mother theory to those which are invariant under the operation of P .
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