Abstract
We propose a lattice field theory formulation which overcomes some fundamental diffculties in realizing exact supersymmetry on the lattice. The Leibniz rule for the difference operator can be recovered by defining a new product on the lattice, the star product, and the chiral fermion species doublers degrees of freedom can be avoided consistently. This framework is general enough to formulate non-supersymmetric lattice field theory without chiral fermion problem. This lattice formulation has a nonlocal nature and is essentially equivalent to the corresponding continuum theory. We can show that the locality of the star product is recovered exponentially in the continuum limit. Possible regularization procedures are proposed.The associativity of the product and the lattice translational invariance of the formulation will be discussed.
Highlights
We have been asking ourselves the following question: "If we stick to keeping exact supersymmetry (SUSY) on the lattice, what kind of lattice formulation are we led to ?" There have been several proposals but they have not been completely successful as general formulations[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
We find a possible answer to our question by introducing on the lattice a new type of product, the star product which is nonlocal in nature but recovers locality exponentially in the continuum limit
We find a lattice formulation which is equivalent to the corresponding continuum theory
Summary
We have been asking ourselves the following question: "If we stick to keeping exact supersymmetry (SUSY) on the lattice, what kind of lattice formulation are we led to ?" There have been several proposals but they have not been completely successful as general formulations[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. There are several difficulties towards exact lattice supersymmetry which are of fundamental nature and intertwined with each other and not easy to solve at the same time. We find a possible answer to our question by introducing on the lattice a new type of product, the star product which is nonlocal in nature but recovers locality exponentially in the continuum limit. The details of the formulation is given in [18]
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