Spontaneous supersymmetry breaking in two dimensional lattice super QCD

Catterall, Simon; Veernala, Aarti

doi:10.1007/jhep10(2015)013

Cited by 19 publications

(27 citation statements)

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“…[150 -152] consider the Berkooz-Douglas matrix model [153], which adds N f fundamental multiplets to Q = 16 SYM QM (preserving half of the supercharges in the continuum). As for the case of two-and three-dimensional SYM, more effort has been devoted to constructing clever lattice formulations of d = 2 and d = 3 SQCD [154 -160] compared to carrying out numerical calculations [161].…”

Section: Challenges For the Futurementioning

confidence: 99%

“…That one numerical calculation [161] uses a generalization of the twisted formulation to realize a quiver construction of two-dimensional Q = 4 SQCD that still preserves one of the supercharges at non-zero lattice spacing [154,155]. The starting point is three-dimensional 8-supercharge SYM on a lattice with only two slices in the third direction.…”

Section: Challenges For the Futurementioning

confidence: 99%

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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%

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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“…• It would be interesting to generalize our lattice model to incorporate matter multiplets along the lines of [13,26] in order to investigate 3d mirror symmetry, whereby two different 3d N = 4 gauge theories flow to the same superconformal fixed point in the IR [27]. Note that under mirror symmetry, Wilson loops are exchanged with vortex loops [28].…”

Section: Resultsmentioning

confidence: 99%

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

Giedt

Lipstein

2018

J. High Energ. Phys.

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In this paper we explore a new approach to studying three-dimensional N = 4 super-Yang-Mills on a lattice. Our strategy is to complexify the Donaldson-Witten twist of four-dimensional N = 2 super-Yang-Mills to make it amenable to a lattice formulation and we find that lattice gauge invariance forces the model to live in at most three dimensions. We analyze the renormalization of the lattice theory and show that uncomplexified three-dimensional N = 4 super-Yang-Mills can be reached in the continuum limit by supplementing the lattice action with appropriate mass terms.

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“…This model was studied with the addition of a Q-invariant FayetIliopoulos term rQ x Tr η(x). 58 The addition of this term allows for dynamical supersymmetry breaking -after integrating out the auxiliary d-field on the U (C) lattice one finds a potential term of the form…”

Section: 4mentioning

confidence: 99%

Supersymmetry on the lattice

Bergner

Catterall

2016

Int. J. Mod. Phys. A

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We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on N = 1 and N = 4 super Yang-Mills in four dimensions. Brief reviews of the corresponding lattice formalisms are given and current results are presented and discussed. We conclude with a summary of the main aspects of current work and prospects for the future.Keywords: Supersymmetry; Lattice quantum field theory; Lattice gauge field theories PACS numbers: 11.15. Ha, 11.30.Pb, 11.25.Tq, 12.38.Gc 1. Why study supersymmetric theories using lattice gauge theory?There are several reasons why supersymmetry has played such an important and prominent role in modern developments of quantum field theory. One is its versatility in constructing extensions of the Standard Model of particle physics. Supersymmetry provides a solution to the hierarchy problem by providing a mechanism for the cancellation of bosonic and fermionic contributions to quantities such as the Higgs mass and as a bonus it includes natural candidates for dark matter. Furthermore, supersymmetric extensions of the standard model have implications at scales that are testable by current collider experiments. At the more fundamental level supersymmetry provides a bridge between the standard model and descriptions of quantum gravity based on supergravity and string theory.Supersymmetric extensions of the standard model like the minimal supersymmetric Standard Model (MSSM) are based on softly broken supersymmetric theories and the relations to the experimental data are usually established by perturbative calculations. In general there are very many of these soft breaking terms (approximately one hundred in the MSSM) and this yields to a lack of predictability in such theories. It is generally believed that such softly broken theories should be thought 1 arXiv:1603.04478v2 [hep-lat]

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Spontaneous supersymmetry breaking in two dimensional lattice super QCD

Cited by 19 publications

References 50 publications

Progress and prospects of lattice supersymmetry

Progress and prospects of lattice supersymmetry

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

Supersymmetry on the lattice

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