Loop formulation of supersymmetric Yang-Mills quantum mechanics

Steinhauer, Kyle; Wenger, Urs

doi:10.1007/jhep12(2014)044

Cited by 16 publications

(28 citation statements)

References 49 publications

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“…So the crucial object for the calculation of the canonical determinants is the product T of the matrices Φ(t) and W (t) which in fact is a product of transfer matrices [8], as was suspected already in [10].…”

Section: Pos(lattice 2015)241mentioning

confidence: 94%

“…In the following we summarise the derivation of the transfer matrices for generic fermion number sectors, recapitulating our results from [8], and show first results for some simple observables such as the Polyakov loop, the moduli of the bosonic fields and the fermion action from simulations in fixed canonical sectors of the theory.…”

Section: Introductionmentioning

confidence: 95%

“…The explicit construction of the fermion transfer matrices for each fermion sector is most easily done via the fermion loop formulation [8] which in essence is an exact (hopping) expansion of the fermionic Boltzmann factor to all orders. In this formulation, the contributions of the fermions to the partition function are obtained by summing over all possible closed oriented fermion loops which are forward propagating in time for any given gauge and boson field background.…”

Section: Transfer Matrices For the Canonical Sectorsmentioning

confidence: 99%

“…and one can use the Cauchy-Binet formula and some further algebra [8] to show that hence the canonical determinant is simply given by the sum over the principal minors of order n f of T denoted by E n f (T ),…”

Section: Transfer Matrices For the Canonical Sectorsmentioning

confidence: 99%

“…The bosonisation of the theory on the lattice by means of the fermion loop formulation [5,6,7] decomposes the fermion contributions into fermion sectors with fixed fermion number. Our recent progress in understanding the algebraic structure of the fermion loop formulation allows the explicit construction of transfer matrices [8]. The transfer matrices in turn provide the starting point for the construction of local fermion update algorithms which allow to directly simulate fixed canonical sectors of the theory.…”

Section: Introductionmentioning

confidence: 99%

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Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

Wenger¹,

Bergner²,

Liu³

2016

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

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The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional reduction in various dimensions and present numerical results for the separate canonical sectors with fixed fermion numbers. We comment on potential problems due to the sign of the contributions from the fermions and due to flat directions.

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Section: Pos(lattice 2015)241mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 95%

Section: Transfer Matrices For the Canonical Sectorsmentioning

confidence: 99%

Section: Transfer Matrices For the Canonical Sectorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

Wenger¹,

Bergner²,

Liu³

2016

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

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$$ \mathcal{N} $$ = 1 Super-Yang-Mills theory on the lattice with twisted mass fermions

Steinhauser

Sternbeck

Wellegehausen

et al. 2021

J. High Energ. Phys.

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Super-Yang-Mills theory (SYM) is a central building block for supersymmetric extensions of the Standard Model of particle physics. Whereas the weakly coupled subsector of the latter can be treated within a perturbative setting, the strongly coupled subsector must be dealt with a non-perturbative approach. Such an approach is provided by the lattice formulation. Unfortunately a lattice regularization breaks supersymmetry and consequently the mass degeneracy within a supermultiplet. In this article we investigate the properties of $$ \mathcal{N} $$ N = 1 supersymmetric SU(3) Yang-Mills theory with a lattice Wilson Dirac operator with an additional parity mass, similar as in twisted mass lattice QCD. We show that a special 45° twist effectively removes the mass splitting of the chiral partners. Thus, at finite lattice spacing both chiral and supersymmetry are enhanced resulting in an improved continuum extrapolation. Furthermore, we show that for the non-interacting theory at 45° twist discretization errors of order $$ \mathcal{O}(a) $$ O a are suppressed, suggesting that the same happens for the interacting theory as well. As an aside, we demonstrate that the DDαAMG multigrid algorithm accelerates the inversion of the Wilson Dirac operator considerably. On a 163× 32 lattice, speed-up factors of up to 20 are reached if commonly used algorithms are replaced by the DDαAMG.

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Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Baumgartner

Wenger

2015

Nuclear Physics B

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Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N = 2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper - the first in a series of three - we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.Comment: 33 pages, 8 figures, 3 tables; typos in text, eq.(107) and table 3 correcte

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Loop formulation of supersymmetric Yang-Mills quantum mechanics

Cited by 16 publications

References 49 publications

Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

$$ \mathcal{N} $$ = 1 Super-Yang-Mills theory on the lattice with twisted mass fermions

Supersymmetric quantum mechanics on the lattice: I. Loop formulation

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