Lattice formulation of 
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 Yang-Mills

Joseph, Anosh

doi:10.1103/physrevd.97.094508

Cited by 2 publications

(2 citation statements)

References 62 publications

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“…It is encouraging that there has been so much recent progress in lattice studies of four-dimensional N = 1 SYM and N = 4 SYM, along with their dimensional reductions to d < 4. This brief overview has also omitted coverage of advances in other areas, including theories without gauge invariance such as Wess-Zumino models and sigma models [162 -166, 171 -174], the lattice regularization of the Green-Schwarz superstring worldsheet sigma model [175 -177], and proposals for lattice formulations of a mass-deformed N = 2 * SYM theory with Q = 8 in four dimensions [178] and of Q = 16 SYM in five dimensions [179]. While there are clear challenges that will be difficult to overcome, in particular concerning supersymmetric QCD and sign problems, overall the prospects of lattice supersymmetry are bright, with many compelling directions for future investigations.…”

Section: Challenges For the Futurementioning

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: Challenges For the Futurementioning

confidence: 99%

Progress and prospects of lattice supersymmetry

Schaich¹

2019

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

View full text Add to dashboard Cite

show abstract

“…In an attempt to understand the role played by cationic and anionic surfactant, hexadecyltrimethylammonium bromide (CTAB) and sodium dodecyl sulfate (SDS) respectively at the interface of MNP core, bare and surfactant modied MNPs were investigated with BSA and dextran molecules. 12,13 Cyclic voltammetry (CV) serves as a fast, simple, sensitive and cost effective technique to study the response of various materials with different analytes. [14][15][16] CV is also helpful in elucidating the reaction mechanism of a system.…”

Section: Introductionmentioning

confidence: 99%