Twisted Supersymmetry on a Lattice

D’Adda, A.; Kanamori, Issaku; Kawamoto, Noboru; Nagata, Kazuhiro

doi:10.1016/j.nuclphysbps.2004.11.118

Cited by 10 publications

(58 citation statements)

References 6 publications

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“…In this section the noncommutativity approach to SUSY on the lattice [3,4,5] is introduced by means of SUSYQM. Periodic boundary conditions will be assumed for all fields.…”

Section: B Definition On the Latticementioning

confidence: 99%

“…The latter also spoils the Leibniz rule for the supercharges which is extensively used to write down supersymmetric actions. D'Adda et al [3,4,5] proposed an approach using noncommutativity between the bosonic and fermionic coordinates in a superspace representation. In this way the Leibniz rule for the supersymmetry transformations is restored and it is in principle possible to define fully supersymmetric lattice actions in a straightforward way, merely copying what is done in the continuum.…”

Section: Introductionmentioning

confidence: 99%

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Noncommutativity approach to supersymmetry on the lattice: Supersymmetric quantum mechanics and an inconsistency

Bruckmann

Kok

2006

Phys. Rev. D

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“…In this section the noncommutativity approach to SUSY on the lattice [3,4,5] is introduced by means of SUSYQM. Periodic boundary conditions will be assumed for all fields.…”

Section: B Definition On the Latticementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Noncommutativity approach to supersymmetry on the lattice: Supersymmetric quantum mechanics and an inconsistency

Bruckmann

Kok

2006

Phys. Rev. D

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“…A part of the exact lattice SUSY of extended algebra was realized and extensively investigated [2,3]. The link approach of super Yang-Mills theory was also proposed [4]. It turned out this formulation needs to be non-commutative and has Hopf algebraic symmetry [5].…”

Section: Introductionmentioning

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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“…A successful formulation of lattice SUSY may be expected to provide a deeper understanding of the relationship between bosons and fermions in a regularized framework. In recent years, it has been recognized that the socalled twisted SUSY formulations are playing particularly important roles in this challenging subject [1,2,3,4,5,6]. It was also recently pointed out that amongst the other formulations of lattice SUSY [7], the deconstruction formulation [8] is quite closely related to the twisted SUSY formulation on the lattice [9].…”

Section: Introductionmentioning

confidence: 99%

“…In the series of papers [1,2,3], we have proposed an extended SUSY formulation on a lattice which keeps all the SUSY transformations exact at least at classical level. The formulation is based on the two crucial theoretical ingredients.…”

Section: Introductionmentioning

confidence: 99%

Exact lattice supersymmetry at largeN

Nagata¹

2008

J. High Energy Phys.

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Employing a novel type of non-commutative product in the Dirac-Kähler twisted superspace on a lattice, we formulate a field theoretically rigid framework of extended supersymmetry on a lattice. As a first example of this treatment, we calculate one-loop (in some cases any loops) quantum corrections for a twisted Wess-Zumino model with N × N hermitian matrix superfields on a two dimensional lattice. The calculations are entirely given in a lattice superfield framework. We report that the mass and the coupling constant are exactly protected from the radiative corrections at non-zero lattice spacing as far as the planar diagrams are concerned, which implies the realization of exact lattice supersymmetry w.r.t. all the supercharges in the large-N limit.

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Twisted Supersymmetry on a Lattice

Cited by 10 publications

References 6 publications

Noncommutativity approach to supersymmetry on the lattice: Supersymmetric quantum mechanics and an inconsistency

Noncommutativity approach to supersymmetry on the lattice: Supersymmetric quantum mechanics and an inconsistency

Summary of Super Doubler Approach on Exact Lattice Supersymmetry

Exact lattice supersymmetry at largeN

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