Advances and applications of lattice supersymmetry

Giedt, Joel

doi:10.22323/1.032.0008

Cited by 26 publications

(33 citation statements)

References 82 publications

(99 reference statements)

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“…(For a recent review, see e.g. [6,7].) Especially, one-dimensional maximally supersymmetric gauge theory has been studied extensively [8,9,10,11,12] and the gauge/gravity duality [4,5] has been confirmed very precisely, including the stringy α ′ corrections [12].…”

Section: Introductionmentioning

confidence: 99%

Lattice study of two-dimensionalN=(2,2)super Yang-Mills theory at largeN

Hanada

Kanamori

2009

Phys. Rev. D

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We study two-dimensional N = (2, 2) SU (N ) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte-Carlo simulation for N = 2, 3, 4, 5 and then extrapolate the result to N = ∞. With the periodic boundary conditions for the fermions along both circles, we establish the existence of a bound state in which scalar fields clump around the origin, in spite of the existence of a classical flat direction. In this phase the global (Z N ) 2 symmetry turns out to be broken. We provide a simple explanation for this fact and discuss its physical implications. *

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Section: Introductionmentioning

confidence: 99%

Lattice study of two-dimensionalN=(2,2)super Yang-Mills theory at largeN

Hanada

Kanamori

2009

Phys. Rev. D

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“…However, the Witten index is not a panacea. There exist physically interesting models for which it is very difficult to determine the Witten index and, in some cases, the index itself might be ill-defined due to a gapless continuous spectrum.In this letter, we consider a possibility to observe the dynamical supersymmetry breaking in euclidean lattice simulations, in the light of recent developments on lattice formulation of supersymmetric theories [2,3,4,5]. The conceptually clearest way to observe the spontaneous supersymmetry breaking would be to examine the degeneracy of bosons' and fermions' mass spectra in two-point correlation functions.…”

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confidence: 99%

Euclidean lattice simulation for dynamical supersymmetry breaking

2008

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The global supersymmetry is spontaneously broken if and only if the ground-state energy is strictly positive. We propose to use this fact to observe the spontaneous supersymmetry breaking in euclidean lattice simulations. For lattice formulations that possess a manifest fermionic symmetry, there exists a natural choice of a hamiltonian operator that is consistent with a topological property of the Witten index. We confirm validity of our idea in models of the supersymmetric quantum mechanics. We then examine a possibility of a dynamical supersymmetry breaking in the twodimensional N = (2, 2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Differently from a recent conjectural claim, our numerical result tempts us to conclude that supersymmetry is not spontaneously broken in this system. PACS numbers: 11.15.Ha, 11.30.Pb, 11.30.Qc It is widely believed that supersymmetry is relevant in particle physics beyond the standard model and it is spontaneously broken by some mechanism. If supersymmetry is not spontaneously broken at the tree level of the loop expansion, it remains so to all orders of the loop expansion. There still exists, however, a possibility that supersymmetry is spontaneously broken nonperturbatively. Precise study of such dynamical supersymmetry breaking remains elusive because we have no universal framework that defines supersymmetric (especially gauge) theories at a non-perturbative level.Generally, the Witten index Tr(−1) F [1], where F is the fermion number operator, provides an important clue. One can infer that the dynamical supersymmetry breaking does not occur in a wide class of supersymmetric models for which the Witten index can be computed to be non-zero. However, the Witten index is not a panacea. There exist physically interesting models for which it is very difficult to determine the Witten index and, in some cases, the index itself might be ill-defined due to a gapless continuous spectrum.In this letter, we consider a possibility to observe the dynamical supersymmetry breaking in euclidean lattice simulations, in the light of recent developments on lattice formulation of supersymmetric theories [2,3,4,5]. The conceptually clearest way to observe the spontaneous supersymmetry breaking would be to examine the degeneracy of bosons' and fermions' mass spectra in two-point correlation functions. Here, we propose an alternative method that is based on the following fact. The global supersymmetry is spontaneously broken if and only if the ground-state energy is strictly positive [6]. In princi- * Electronic address: kanamori-i@riken.jp † Electronic address: hsuzuki@riken.jp ‡ Electronic address: fumihiko˙sugino@pref.okayama.lg.jp ple, therefore, one can judge whether the supersymmetry breaking takes place or not if the ground-state energy can be computed. Let us first recall that the thermal average of the hamiltonian H with the inverse temperature β is expressed by the euclidean functional integral as [22] Tr He −βH Tr e −βH = aPBC dµ He −S aPBC ...

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“…However, introducing fundamental matter, as will be explained in section 3, turns out to be a difficult task. 2 In this paper, we show that quiver and Chern-Simons gauge theories can be regularized using the techniques of [16]. More specifically, in section 3 we construct the supersymmetric U(N )×U(M ) gauge theory with bifundamental matter.…”

Section: Jhep11(2009)087mentioning

confidence: 99%

“…To understand their nonperturbative aspects, one might expect lattice simulation to be useful as it happens in the usual non-supersymmetric gauge theories. However, it is generally difficult to realize SYM on lattices and consequently detailed numerical simulations have been performed only in lower (less than four) dimensions (see [1] for recent simulations of 4d SYM, and [2] for a review of lattice supersymmetry).…”

Section: Introductionmentioning

confidence: 99%