Real space renormalization group for twisted lattice N $$ \mathcal{N} $$ =4 super Yang-Mills

Catterall, Simon; Giedt, Joel

doi:10.1007/jhep11(2014)050

Cited by 26 publications

(48 citation statements)

References 24 publications

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“…[16]. These investigations, as well as finite-size scaling and Monte Carlo renormalization group [18] analyses of the scaling dimensions of simple conformal operators, will soon be reported in future work.…”

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confidence: 87%

Aspects of lattice N=4 supersymmetric Yang–Mills

Schaich

2016

Proceedings of the 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)

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Non-perturbative investigations of N = 4 supersymmetric Yang-Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.

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confidence: 87%

Aspects of lattice N=4 supersymmetric Yang–Mills

Schaich

2016

Proceedings of the 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)

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“…Additional supersymmetry-violating operators include fermion (quark and gaugino) mass terms, Yukawa couplings, and quartic (fourscalar) terms. Altogether there are typically O(10) of these operators [3,14,15], implying such high-dimensional parameter spaces that there seems to be little hope of effectively navigating them in numerical lattice calculations.…”

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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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“…Breaking the U (1) symmetry is likely harmless since the U (1) sector plays no role in the continuum limit. However breaking the exact supersymmetry is more problematic since it invalidates the arguments given in [30] devoted to the renormalizability of the lattice theory and specifically the number of counterterms needed to tune to a supersymmetric continuum limit.…”

Section: Lattice Actionmentioning

confidence: 99%

Removal of the trace mode in lattice N=4 super Yang-Mills theory

2018

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Twisted and orbifold formulations of lattice N = 4 super Yang-Mills theory which possess an exact supersymmetry require a U (N ) = SU (N ) ⊗ U (1) gauge group. In the naive continuum limit, the U (1) modes trivially decouple and play no role in the theory. However, at non-zero lattice spacing they couple to the SU (N ) modes and can drive instabilities in the lattice theory.For example, it is well known that the lattice U (1) theory undergoes a phase transition at strong coupling to a chirally broken phase. An improved action that suppresses the fluctuations in the U (1) sector was proposed in [1]. Here, we explore a more aggressive approach to the problem by adding a term to the action which can entirely suppress the U (1) mode. The penalty is that the new term breaks the Q-exact lattice supersymmetry. However, we argue that the term is 1/N 2 suppressed and the existence of a supersymmetric fixed point in the planar limit ensures that any SUSY-violating terms induced in the action possess couplings that also vanish in this limit. We present numerical results on supersymmetric Ward identities consistent with this conclusion.

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Real space renormalization group for twisted lattice N $$ \mathcal{N} $$ =4 super Yang-Mills

Cited by 26 publications

References 24 publications

Aspects of lattice N=4 supersymmetric Yang–Mills

Aspects of lattice N=4 supersymmetric Yang–Mills

Progress and prospects of lattice supersymmetry

Removal of the trace mode in lattice N=4 super Yang-Mills theory

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