3d $$ \mathcal{N}=4 $$ super-Yang-Mills on a lattice

Giedt, Joel; Lipstein, Arthur E.

doi:10.1007/jhep03(2018)162

Cited by 4 publications

(3 citation statements)

References 34 publications

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“…Here we will highlight the numerical calculations, which leaves little to say about d = 3: see Refs. [18,51,52] for Q = 8 formulations.…”

Section: +1 Dimensionsmentioning

confidence: 99%

Progress and prospects of lattice supersymmetry

Schaich¹

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model, while lattice field theory provides a nonperturbative regularization suitable for strongly interacting systems. Lattice investigations of supersymmetric field theories are currently making significant progress, though many challenges remain to be overcome. In this brief overview I discuss particularly notable progress in three areas: supersymmetric Yang-Mills (SYM) theories in fewer than four dimensions, as well as both minimal N = 1 SYM and maximal N = 4 SYM in four dimensions. I also highlight super-QCD and sign problems as prominent challenges that will be important to address in future work. Progress and prospects of lattice supersymmetry David Schaich Introduction, motivation and backgroundSupersymmetry plays prominent roles in modern theoretical physics, as a tool to improve our understanding of quantum field theory (QFT), as an ingredient in many new physics models, and as a means to study quantum gravity via holographic duality. Lattice field theory provides a nonperturbative regularization for QFTs, and other contributions to these proceedings document the prodigious success of this framework applied to QCD and similar theories. It is natural to consider employing lattice field theory to investigate supersymmetric QFTs, especially in strongly coupled regimes. In this proceedings I review the recent progress and future prospects of lattice studies of supersymmetric systems, focusing on four-dimensional gauge theories and their dimensional reductions to d < 4. 1 Lattice supersymmetry now has more than four decades of history [1], much of which is reviewed by Refs. [2 -7]. Unfortunately, progress in this field has been slower than for QCD, in large part because the lattice discretization of space-time breaks supersymmetry. This occurs in three main ways. First, the anti-commutation relation Q α , Qα = 2σ µ αα P µ in the super-Poincaré algebra connects the spinorial generators of supersymmetry transformations, Q α and Qα, to the generator of infinitesimal space-time translations, P µ . The absence of infinitesimal translations on the lattice consequently implies broken supersymmetry.Next, bosonic and fermionic fields are typically discretized differently on the lattice (in part due to the famous fermion doubling problem). In the specific context of supersymmetric gauge theories, standard discretizations associate the gauginos with lattice sites n (i.e., they transform as G(n)λ α (n)G † (n) under a lattice gauge transformation) while the gauge connections are associated with links between nearest-neighbor sites, transforming as G(n)U µ (n)G † (n + a µ) where 'a' is the lattice spacing. Away from the a → 0 continuum limit, these differences prevent supersymmetry transformations from correctly interchanging superpartners.Finally, supersymmetry requires a derivative operator that obeys the Leibniz rule [1], viz. ∂ [φη] = [∂φ] η + φ∂η, which is violated by standard la...

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“…Here we will highlight the numerical calculations, which leaves little to say about d = 3: see Refs. [18,51,52] for Q = 8 formulations.…”

Section: +1 Dimensionsmentioning

confidence: 99%

Progress and prospects of lattice supersymmetry

Schaich¹

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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“…Supersymmetry-preserving twisted formulations (discussed by Refs. [25,116,117]) are even more important than in two dimensions, and are used by all numerical calculations so far [118,119]. Figure 2 presents some results from these works, investigating the Q = 16 SYM bosonic action that holography relates to the internal energy of the dual black brane geometry in supergravity.…”

Section: +1 Dimensionsmentioning

confidence: 99%

Lattice studies of supersymmetric gauge theories

Schaich¹

2022

Preprint

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Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model. Lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems. This invited review briefly summarizes significant recent progress in lattice investigations of supersymmetric field theories, as well as some of the challenges that remain to be overcome. I focus on progress in three areas: supersymmetric Yang-Mills (SYM) theories in fewer than four space-time dimensions, as well as both minimal N = 1 SYM and maximal N = 4 SYM in four dimensions. I also highlight superQCD and sign problems as prominent challenges that will be important to address in future work.

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“…This was the basis of our lattice formulation in [4]. An alternative, Blau-Thompson, twist [5] is used in [6].…”

Section: Continuum Theorymentioning

confidence: 99%

Lattice ${\cal N}=4$ three-dimensional super-Yang-Mills

Giedt¹,

Lipstein²,

Martin³

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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We describe our recent work on the lattice formulation of N = 4 three-dimensional super-Yang-Mills. Our formulation was based on the Donaldson-Witten twist, but we have also been studying the formulation based on the Blau-Thompson twist by Joseph. We find in the latter case there is a single counterterm necessary to restore supersymmetry in the continuum limit, and that this counterterm can be computed with a two-loop calculation in lattice perturbation theory. It is crucial that this three-dimensional model is super-renormalizable. We also describe some of the motivations for studying three-dimensional theories, including mirror symmetry and holographic cosmology.

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3d $$ \mathcal{N}=4 $$ super-Yang-Mills on a lattice

Cited by 4 publications

References 34 publications

Progress and prospects of lattice supersymmetry

Progress and prospects of lattice supersymmetry

Lattice studies of supersymmetric gauge theories

Lattice ${\cal N}=4$ three-dimensional super-Yang-Mills

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