4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow

Hieda, Kenji; Kasai, Aya; Makino, Hiroki; Suzuki, Hiroshi

doi:10.1093/ptep/ptx073

Cited by 22 publications

(31 citation statements)

References 46 publications

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“…thermal and periodic boundary conditions (BCs) for the gauginos, they find evidence that periodic BCs allow the confined, chirally broken phase to persist for weak couplings where analytic semiclassical methods [118] may be reliable. In addition, there is ongoing work to construct a SYM gradient flow that is consistent with supersymmetry in Wess-Zumino gauge [119], which could be used to define a renormalized supercurrent and help guide fine-tuning [120,121]. The ordinary non-supersymmetric gradient flow is already used by many lattice N = 1 SYM projects, to set the scale (as in the right plot of Fig.…”

Section: Minimally Supersymmetric Yang-mills (N = 1 Sym) In Four Dimementioning

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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Section: Minimally Supersymmetric Yang-mills (N = 1 Sym) In Four Dimementioning

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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“…Therefore, as in Ref. [8], we will be satisfied by finding the form of a properly normalized supercurrent that works within the on-mass-shell correlation functions containing gauge-invariant operators. By "on-mass-shell," we mean that all (renormalized) composite operators including the combination in Eq.…”

Section: Properly Normalized Supercurrentmentioning

confidence: 97%

“…Our strategy is basically identical to that of Ref. [8]: First, we need the expression of the properly normalized conserved supercurrent with a certain regularization. As noted in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang–Mills supercurrent

Kasai

Morikawa

Suzuki

2018

Progress of Theoretical and Experimental Physics

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063B03 (2017), a properly normalized supercurrent in the four-dimensional (4D) N = 1 super Yang-Mills theory (SYM) that works within on-mass-shell correlation functions of gauge-invariant operators is expressed in a regularization-independent manner by employing the gradient flow. In the present paper, this construction is extended to the supercurrent in the 4D N = 2 SYM. The so-constructed supercurrent will be useful, for instance, for fine tuning of lattice parameters toward the supersymmetric continuum limit in future lattice simulations of the 4D N = 2 SYM.

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“…In super Yang-Mills (SYM), the most naive approach is to use a non-SUSY flow, which consists of the Yang-Mills flow and an adjoint matter flow [4] although SUSY is broken at a nonzero flow time. From this point of view, a lattice simulation of N = 1 SYM has been carried out in [35] and the regularization independent definition of the supercurrent in N = 1, 2 SYM has been given in [36,37].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric gradient flow in the Wess-Zumino model

2019

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We propose a supersymmetric gradient flow equation in the four-dimensional Wess-Zumino model. The flow is constructed in two ways. One is based on the off-shell component fields and the other is based on the superfield formalism, in which the same result is provided. The obtained flow is supersymmetric because the flow time derivative and the supersymmetry transformation commute with each other. Solving the equation, we find that it has a damping oscillation with the flow time for nonzero mass, which is different from the Yang-Mills flow. The on-shell flow equation is also discussed.

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4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow

Cited by 22 publications

References 46 publications

Progress and prospects of lattice supersymmetry

Progress and prospects of lattice supersymmetry

Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang–Mills supercurrent

Supersymmetric gradient flow in the Wess-Zumino model

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