Mass spectrum of 2-dimensional $$ \mathcal{N}=\left(2,2\right) $$ super Yang-Mills theory on the lattice

August, Daniel; Steinhauser, M.; Wellegehausen, Björn; Wipf, Andreas

doi:10.1007/jhep01(2019)099

Cited by 13 publications

(11 citation statements)

References 79 publications

(125 reference statements)

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“…However, e iα pq is expected to decrease exponentially in the lattice volume, and the situation is likely to be worse for SQCD. Directly evaluating the pfaffian is much more computationally expensive, and has been done mostly for SYM QM and d = 2 SYM, where sign problems also appear to be well under control [36,38,80,81,86,95,97]. Figure 5 presents results for the pfaffian phase of lattice N = 4 SYM in four dimensions, adapted from Refs.…”

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)

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“…See Ref. [2][3][4] for discussions and references therein. * smcatter@syr.edu † rgjha@syr.edu ‡ anosh.joseph@icts.res.in…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative study of dynamical SUSY breaking in N=(2,2) Yang-Mills theory

Catterall¹,

Jha²,

Joseph³

2018

Phys. Rev. D

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We examine the possibility of dynamical supersymmetry breaking in two-dimensional N ¼ ð2; 2Þ supersymmetric Yang-Mills theory. The theory is discretized on a Euclidean spacetime lattice using a supersymmetric lattice action. We compute the vacuum energy of the theory at finite temperature and take the zero-temperature limit. Supersymmetry will be spontaneously broken in this theory if the measured ground-state energy is nonzero. By performing simulations on a range of lattices up to 96 × 96 we are able to perform a careful extrapolation to the continuum limit for a wide range of temperatures. Subsequent extrapolations to the zero-temperature limit yield an upper bound on the ground-state energy density. We find the energy density to be statistically consistent with zero in agreement with the absence of dynamical supersymmetry breaking in this theory.

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“…There have also been some noteworthy numerical studies of non-maximal N = (2, 2) SYM[38][39][40][41][42][43][44][45][46][47][48][49][50][51] and super-QCD[52] in two dimensions.…”

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confidence: 99%

Testing holography using lattice super-Yang-Mills theory on a 2-torus

et al. 2018

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We consider maximally supersymmetric SUðNÞ Yang-Mills theory in Euclidean signature compactified on a flat two-dimensional torus with antiperiodic ("thermal") fermion boundary conditions imposed on one cycle. At large N, holography predicts that this theory describes certain black hole solutions in type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N ¼ 16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory-Laflamme transition.

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Mass spectrum of 2-dimensional $$ \mathcal{N}=\left(2,2\right) $$ super Yang-Mills theory on the lattice

Cited by 13 publications

References 79 publications

Progress and prospects of lattice supersymmetry

Progress and prospects of lattice supersymmetry

Nonperturbative study of dynamical SUSY breaking in N=(2,2) Yang-Mills theory

Testing holography using lattice super-Yang-Mills theory on a 2-torus

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