Supersymmetric gradient flow in the Wess-Zumino model

Kadoh, Daisuke; Kikuchi, Kengo; Ukita, N.

doi:10.1103/physrevd.100.014501

Cited by 16 publications

(16 citation statements)

References 53 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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“…The application for supersymmetric theories has been suggested in [14,15], where it can help to renormalize the supercurrent. In several works also a supersymmetric version of the method has been developed [16,17], which might even avoid the necessity of a multiplicative renormalization of the fermions. In this contribution we present an extended study of the phase diagram of N = 1 SYM with the gauge group SU(2) at zero and non-zero temperature.…”

Section: Introductionmentioning

confidence: 99%

Study of center and chiral symmetry realization in thermal N=1 super Yang-Mills theory using the gradient flow

Bergner¹,

Lopez²,

Piemonte³

2019

Phys. Rev. D

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The realization of center and chiral symmetries in N = 1 super Yang-Mills theory (SYM) is investigated on a four-dimensional Euclidean lattice by means of Monte Carlo methods. At zero temperature this theory is expected to confine external fundamental charges and to have a non-vanishing gaugino condensate, which breaks the non-anomalous Z 2Nc chiral symmetry. In previous studies at finite temperatures, the phase transitions corresponding to deconfinement and chiral restoration were observed to occur at roughly the same critical temperature for SU(2) gauge group. We find further evidences for this observation from new measurements at smaller lattice spacings using the fermion gradient flow, and we discuss the agreement of our findings with conjectures from superstring theory. The implementation of the gradient flow technique allows us also to estimate, for the first time, the condensate at zero temperatures and zero gaugino mass with Wilson fermions.

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“…1 See [12] for the SUSY gradient flow in the Wess-Zumino model. 2 We basically follow the notation used in Ref.…”

Section: Sqcd In the Superfield Formalismmentioning

confidence: 99%

“…On the other hand, a SUSY flow is defined by the gradient of the SYM action with respect to a vector superfield [9]. The latter flow can be given for the component fields in a gauge covariant and supersymmetric manner [10], and the finiteness of flowed field correlators can be shown for the whole gauge supermultiplet [11]. 1 In this paper, a SUSY gradient flow is derived for N = 1 SQCD in four dimensions.…”

Section: Introductionmentioning

confidence: 99%

Gradient flow equation in SQCD

Kadoh¹,

Ukita²

2020

Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

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We propose a supersymmetric gradient flow in N = 1 SQCD in four dimensions. The flow equation is derived in the superfield formalism and is also given for component fields of the Wess-Zumino gauge in a gauge covariant manner. We find that the flow for the component fields is supersymmetric in a sense that the flow time derivative and any supersymmetry transformation commute with each other up to a gauge transformation.

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Supersymmetric gradient flow in the Wess-Zumino model

Cited by 16 publications

References 53 publications

Progress and prospects of lattice supersymmetry

Progress and prospects of lattice supersymmetry

Study of center and chiral symmetry realization in thermal N=1 super Yang-Mills theory using the gradient flow

Gradient flow equation in SQCD

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