Twisted superspace on a lattice

Abstract

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 noncommutativity 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 noncommutativity 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.

N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

“…The details of the twisted chiral superfield formulation for N = D = 2 can be found in [50,63]. The reason why we call these condition as the chiral condition stems from the DiracKähler fermion formulation on a lattice.…”

“…The details of the twisted chiral superfield formulation for N = D = 2 can be found in [50,63]. Then the bi-linear product of the twisted chiral and anti-chiral superfields leads to an off-shell N = 2 twisted SUSY invariant action…”

“…It is well known that the Dirac-Kähler fermion mechanism is fundamentally related to the lattice formulation [64][65][66] [67,68]. In fact recently N = 2 twisted superspace in two dimensions has been successfully formulated on a lattice with an introduction of mild non-commutability [69][70][71][72][73][74] for lattice difference operator and twisted supercharges [63]. It is strongly suggested that N = 4 twisted superspace formalism in four dimensions is important to formulate four-dimensional SUSY on a lattice.…”

Mass deformation of twisted super Yang-Mills theory with fuzzy sphere solution

“…Full SUSY will, then, be recovered at continuum limit without any fine-tuning [10][11][12][13]. While there is another ambitious approach, called link approach [14,15], which claims the model can be exactly full supersymmetric even on the lattice. Besides it suggests the relationship between the noncommutativity in the link approach and the nonlocality in a new formulation [16].…”

Lattice formulation of (2,2) supersymmetric gauge theories with matter fields

“…This work was foreshadowed by an early proposal to use Dirac-Kähler fermions in the construction of a supersymmetric lattice Hamiltonian in one spatial dimension [17]. A more ambitious construction which purports to preserve all supercharges on the lattice has been proposed [18][19][20][21][22], but remains controversial [23].…”