Exact lattice supersymmetry at the quantum level for N = 2 Wess–Zumino models in 1- and 2-dimensions

Asaka, Keisuke; D’Adda, A.; Kawamoto, Noboru; Kondo, Yoshi

doi:10.1142/s0217751x16501256

Cited by 9 publications

(14 citation statements)

References 93 publications

(95 reference statements)

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“…In fact we found a formulation of the N = 2 Wess-Zumino models in one and two dimensions which have exact SUSY on the lattice [16,17]. It has been also confirmed that SUSY on the lattice is preserved even at the quantum level [19]. It has, however, been recognized that associativity for the -product is broken:…”

Section: Difficulties Of Lattice Susy and The Possible Solutionssupporting

confidence: 57%

“…In order to recover the associativity for the -product we notice that if momentap i does not have upper limit in (18); then 2 a is replaced by ∞ in (19) and associativity is recovered. For this reason we tried to find an alternative lattice translation generator ∆(p) with the following properties:…”

Section: Difficulties Of Lattice Susy and The Possible Solutionsmentioning

confidence: 99%

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An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry-Summary of the Formulation-

2018

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Abstract. We propose a lattice field theory formulation which overcomes some fundamental difficulties 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.

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Section: Difficulties Of Lattice Susy and The Possible Solutionssupporting

confidence: 57%

Section: Difficulties Of Lattice Susy and The Possible Solutionsmentioning

confidence: 99%

An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry-Summary of the Formulation-

2018

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“…Non-associativity does not sacrifice exact lattice SUSY for non-gauge cases. In fact exact SUSY has been confirmed even at the quantum level [15]. We have proposed a new lattice SUSY formulation by the use of ∆ G as a differential operator.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Summary of Super Doubler Approach on Exact Lattice Supersymmetry

D’Adda¹,

Kawamoto²,

Saito³

2016

Proceedings of the 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)

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We have proposed a lattice SUSY formulation which we may call super doubler approach, where chiral fermion species doublers and their bosonic counter parts are either identified as super partners or truncated by chiral conditions. We claim that the super symmetry is exactly kept on the lattice. However the formulation is nonlocal and breaks lattice translational invariance. We argue that these features cause no fundamental difficulties in the continuum limit. Although a naive version of this formulation breaks associativity of the product of fields we have found a modified super doubler approach that recovers the associativity and is applicable to super Yang-Mills theory. It turns out that this formulation is essentially equivalent to the continuum formulation and thus keeps all the symmetry exact even at a finite lattice constant. Inspired by this formulation we propose a non-local lattice field theory formulation which is free of chiral fermion problem and has the same exact lattice symmetry as continuum theory.

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“…Nevertheless the resulting lattice theories had exact supersymmetry, even at the quantum level [51].…”

Section: Jhep12(2017)089mentioning

confidence: 99%

An alternative lattice field theory formulation inspired by lattice supersymmetry

D’Adda

Kawamoto

Saito

2017

J. High Energ. Phys.

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Abstract:We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree of freedom on the lattice corresponds to 2 d degrees of freedom in the continuum, but all these doublers have (in the case of fermions) the same chirality and can be either identified, thus removing the degeneracy, or, in some theories with extended supersymmetry, identified with different members of the same supermultiplet. 2) The derivative operator, defined on the lattice as a suitable periodic function of the lattice momentum, is an addittive and conserved quantity, thus assuring that the Leibniz rule is satisfied. This implies that the product of two fields on the lattice is replaced by a non-local "star product" which is however in general nonassociative. Associativity of the "star product" poses strong restrictions on the form of the lattice derivative operator (which becomes the inverse Gudermannian function of the lattice momentum) and has the consequence that the degrees of freedom of the lattice theory and of the continuum theory are in one-to-one correspondence, so that the two theories are eventually equivalent. We can show that the non-local star product of the fields effectively turns into a local one in the continuum limit. Regularization of the ultraviolet divergences on the lattice is not associated to the lattice spacing, which does not act as a regulator, but may be obtained by a one parameter deformation of the lattice derivative, thus preserving the lattice structure even in the limit of infinite momentum cutoff. However this regularization breaks gauge invariance and a gauge invariant regularization within the lattice formulation is still lacking.

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Exact lattice supersymmetry at the quantum level for N = 2 Wess–Zumino models in 1- and 2-dimensions

Cited by 9 publications

References 93 publications

An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry-Summary of the Formulation-

An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry-Summary of the Formulation-

Summary of Super Doubler Approach on Exact Lattice Supersymmetry

An alternative lattice field theory formulation inspired by lattice supersymmetry

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