Progress in Four-Dimensional Lattice Supersymmetry

Giedt, Joel

doi:10.1142/s0217751x09045492

Cited by 44 publications

(57 citation statements)

References 179 publications

(298 reference statements)

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“…See also the recent reviews [15,16] for further references. In addition, there has recently been a great deal of other work, both theoretical and numerical, focused on discrete formulations of N = 4 SYM see Refs.…”

Section: Introductionmentioning

confidence: 99%

Perturbative renormalization of lattice $ \mathcal{N} = 4 $ super Yang-Mills theory

Catterall

Dzienkowski

Giedt

et al. 2011

J. High Energ. Phys.

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We consider N = 4 super Yang-Mills theory on a four-dimensional lattice. The lattice formulation under consideration retains one exact supersymmetry at non-zero lattice spacing. We show that this feature combined with gauge invariance and the large point group symmetry of the lattice theory ensures that the only counterterms that appear at any order in perturbation theory correspond to renormalizations of existing terms in the bare lattice action. In particular we find that no mass terms are generated at any finite order of perturbation theory. We calculate these renormalizations by examining the fermion and auxiliary boson self energies at one loop and find that they all exhibit a common logarithmic divergence which can be absorbed by a single wavefunction renormalization. This finding implies that at one loop only a fine tuning of the finite parts is required to regain full supersymmetry in the continuum limit.

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Section: Introductionmentioning

confidence: 99%

Perturbative renormalization of lattice $ \mathcal{N} = 4 $ super Yang-Mills theory

Catterall

Dzienkowski

Giedt

et al. 2011

J. High Energ. Phys.

Self Cite

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“…In order to study N = 4 SYM in the strongly coupled region, one needs to have a non-perturbative formulation such as the lattice gauge theory. In fact, there are considerable developments in the lattice theories of N = 4 SYM [4][5][6][7][8][9][10][11]. However, any lattice formulations of N = 4 SYM proposed so far seem to require the fine-tuning of at least three parameters 1 .…”

Section: Introductionmentioning

confidence: 99%

Perturbative tests for a large-N reduced model of $ \mathcal{N} = {4} $ super Yang-Mills theory

Ishiki

Shimasaki

Tsuchiya

2011

J. High Energ. Phys.

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We study a non-perturbative formulation of N = 4 super Yang-Mills theory (SYM) on R × S 3 proposed in arXiv:0807.2352. This formulation is based on the large-N reduction, and the theory can be described as a particular large-N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3 . In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.

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“…Non-perturbative dynamics play an important role in the theory of supersymmetry breaking needed in order to produce a low-energy four-dimensional effective action with a residual N = 1 supersymmetry. For this reason, much effort has been dedicated to formulating a lattice version of supersymmetric theories (see [1][2][3][4][5][6]). …”

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confidence: 99%

Two-loop Wess-Zumino model with exact supersymmetry on the lattice

Feo

2013

Phys. Rev. D

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We consider a lattice formulation of the four dimensional N = 1 Wess-Zumino model in terms of the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. The lattice action is invariant under a deformed supersymmetric transformation which is non-linear in the scalar fields and it is determined by an iterative procedure in the coupling constant to all orders in perturbation theory. We also show that the corresponding Ward-Takahashi identity is satisfied at fixed lattice spacing. The calculation is performed in lattice perturbation theory up to order g 3 (two-loop) and the Ward-Takahashi identity (containing 110 connected non-tadpole Feynman diagrams) is satisfied at fixed lattice spacing thanks to this exact lattice supersymmetry.

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Progress in Four-Dimensional Lattice Supersymmetry

Cited by 44 publications

References 179 publications

Perturbative renormalization of lattice $ \mathcal{N} = 4 $ super Yang-Mills theory

Perturbative renormalization of lattice $ \mathcal{N} = 4 $ super Yang-Mills theory

Perturbative tests for a large-N reduced model of $ \mathcal{N} = {4} $ super Yang-Mills theory

Two-loop Wess-Zumino model with exact supersymmetry on the lattice

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