Lattice chiral symmetry, Yukawa couplings and the Majorana condition

Fujikawa, Kazuo; Ishibashi, Masato

doi:10.1016/s0370-2693(02)01230-3

Cited by 40 publications

(51 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, even if the actual value for the ratio K (1) /K (2) were 3σ greater than the current estimate, the divergence of the supercurrent is an order of magnitude smaller for the action (2.7) than for the action (2.8).…”

Section: Nonperturbative Analysiscontrasting

confidence: 71%

“…Thus, as has been discussed originally in [1], and at greater length in [2,5] the action is singular once auxiliary fields are integrated out. However, as we described in [25], there is a sensible resolution of this singularity by taking the theory to "live" inside a finite box, with antiperiodic boundary conditions in the time direction for the fermions.…”

Section: A Summary Of Our Previous Workmentioning

confidence: 89%

“…Theories such as super-QCD and N = 4 super-Yang-Mills are of particular interest, but it seems wise to refine methods using simpler toy models such as the Wess-Zumino model, given the difficulties with supersymmetry on the lattice. Hence, we continue our investigations of a lattice formulation that was studied by several groups a few years ago [1][2][3][4][5][6]. What we are developing here is a methodology for analyzing the extent to which supersymmetry is a feature of the low energy effective theory.…”

mentioning

confidence: 92%

See 2 more Smart Citations

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

2011

View full text Add to dashboard Cite

We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U (1) R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.

show abstract

Section: Nonperturbative Analysiscontrasting

confidence: 71%

Section: A Summary Of Our Previous Workmentioning

confidence: 89%

mentioning

confidence: 92%

See 1 more Smart Citation

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

2011

View full text Add to dashboard Cite

show abstract

“…This action makes use of Ginsparg-Wilson fermions, so that the U(1) R symmetry of the massless theory is respected without fine-tuning [69][70][71]. While the nonlocal exact lattice supersymmetry proposed by Bonini and Feo is a symmetry of the partition function, order by order, it remains to be seen what it has to do with symmetries of the tranfer matrix, and hence Hamiltonian.…”

Section: Nonlinear Q Modelsmentioning

confidence: 99%

Deconstruction and Other Approaches to Supersymmetric Lattice Field Theories

Giedt

2006

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.

show abstract

“…Modern resolution of chiral fermion problem for QCD may give a suggestion that Ginsparg-Wilson fermion would solve lattice SUSY fermion treatment. It was pointed out that Majorana condition has a difficulty of compatibility with Ginsparg-WiIson relation [12]. After all in these formulations fermions are formulated differently from bosons the realization of exact lattice SUSY is difficult.…”

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)

View full text Add to dashboard Cite

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.

show abstract

Lattice chiral symmetry, Yukawa couplings and the Majorana condition

Cited by 40 publications

References 45 publications

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

Deconstruction and Other Approaches to Supersymmetric Lattice Field Theories

Summary of Super Doubler Approach on Exact Lattice Supersymmetry

Contact Info

Product

Resources

About