Improved results for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>super Yang-Mills theory using supersymmetric discrete light-cone quantization

Harada, Motomichi; Hiller, John R.; Pinsky, Stephen S.; Salwen, Nathan

doi:10.1103/physrevd.70.045015

Cited by 15 publications

(6 citation statements)

References 30 publications

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“…Indeed, if we add some finite terms present in the full Hamiltonian (5), we see that these state acquire a non-zero energy. At least in our approximation we find no evidence (apart from the just mentioned states) for the absence of a mass gap reported in some previous studies [18]. We also see clearly how the existence of many other massless states, for each value of R, is nothing but a consequence of the breakdown of the method when the number of partons approaches its maximal value compatible with momentum conservation.…”

Section: Discussioncontrasting

confidence: 55%

“…As we will see in the following sections one can compactify also the x − direction and replace all the integrals ∞ 0 dk with sums over positive integers ∞ n=1 , the key point is precisely that all LC momenta have to be greater than zero, so we can actually rewrite ∞ 0 dk = +∞ −∞ dk θ(k). We note, incidentally that in [18] it was claimed that the discretized version of the supercharges does not satisfy the susy algebra. We claim instead that everything works fine provided an appropriate care is used in performing the discretization and in defining the (anti)commutators; particular attention is needed when, by momentum conservation, an intermediate parton gets a vanishing momentum: by adopting a careful prescription for the ensuing θ(0) we can fully maintain supersymmetry.…”

Section: Light-cone Sym 4 and Its Dimensional Reductionmentioning

confidence: 91%

“…Many other massless states have been found in the literature[18] for any K . These are due to a finite-K artifact by which states with a large number of partons, k ∼ K, are annihilated by the SUSY charges (and therefore by the Hamiltonian), since all transitions are blocked by the finite momentum resolution.…”

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confidence: 95%

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Dimensionally reduced SYM4 at large-N: an intriguing Coulomb approximation

Dorigoni

Veneziano

Wosiek

2011

J. High Energ. Phys.

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Abstract:We consider the light-cone (LC) gauge and LC quantization of the dimensional reduction of super Yang Mills theory from four to two dimensions. After integrating out all unphysical degrees of freedom, the non-local LC Hamiltonian exhibits an explicit N = (2, 2) supersymmetry. A further SUSY-preserving compactification of LC-space on a torus of radius R, allows for a large-N numerical study where the smooth large-R limit of physical quantities can be checked. As a first step, we consider a simple, yet quite rich, "Coulomb approximation" that maintains an N = (1, 1) subgroup of the original supersymmetry and leads to a non-trivial generalization of 't Hooft's model with an arbitrary -but conservednumber of partons. We compute numerically the eigenvalues and eigenvectors both in momentum and in position space. Our results, so far limited to the sectors with 2, 3 and 4 partons, directly and quantitatively confirm a simple physical picture in terms of a string-like interaction with the expected tension among pairs of nearest-neighbours along the single-trace characterizing the large-N limit. Although broken by our approximation, traces of the full N = (2, 2) supersymmetry are still visible in the low-lying spectrum.

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Section: Discussioncontrasting

confidence: 55%

Section: Light-cone Sym 4 and Its Dimensional Reductionmentioning

confidence: 91%

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Dimensionally reduced SYM4 at large-N: an intriguing Coulomb approximation

Dorigoni

Veneziano

Wosiek

2011

J. High Energ. Phys.

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“…Supersymmetric Yang-Mills theories in extended space have been studied for some time with the aid of the Hamiltonian approach on the light cone [29]. 2 The system and early results…”

Section: Introductionmentioning

confidence: 99%

High precision study of the structure of supersymmetric Yang–Mills quantum mechanics

Campostrini

Wosiek

2004

Nuclear Physics B

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The spectrum of D = 4 supersymmetric Yang-Mills quantum mechanics is computed with high accuracy in all channels of angular momentum and fermion number. Localized and non-localized states coexists in certain channels as a consequence of the supersymmetric interactions with flat valleys. All states fall into well identifiable supermultiplets providing an explicit realization of supersymmetry on the spectroscopic level. An accidental degeneracy among some supermultiplets has been found. Regularized Witten index converges to a time-independent constant which agrees with earlier calculations.

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“…Apart from being a descendant of SYM theory in four dimensions, the N = (2, 2) theory in two dimensions has further interesting properties. Theoretical arguments [24,25] and numerical calculations based on a discretized light cone quantization [26,27], both suggest massless states in the physical spectrum. This massless super-multiplet is not seen in four dimensions.…”

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confidence: 99%

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

August

Steinhauser

Wellegehausen

et al. 2019

J. High Energ. Phys.

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In the present work we analyse N = (2, 2) supersymmetric Yang-Mills (SYM) theory with gauge group SU (2) in two dimensions by means of lattice simulations. The theory arises as dimensional reduction of N = 1 SYM theory in four dimensions. As in other gauge theories with extended supersymmetry, the classical scalar potential has flat directions which may destabilize numerical simulations. In addition, the fermion determinant need not be positive and this sign-problem may cause further problems in a stochastic treatment. We demonstrate that N = (2, 2) super Yang-Mills theory has actually no sign problem and that the flat directions are lifted and thus stabilized by quantum corrections. Only the bare mass of the scalars experience a finite additive renormalization in this finite theory. On various lattices with different lattice constants we determine the scalar masses and hopping parameters for which the supersymmetry violating terms are minimal. By studying four Ward identities and by monitoring the π-mass we show that supersymmetry is indeed restored in the continuum limit. In the second part we calculate the masses of the low-lying bound states. We find that in the infinite-volume and supersymmetric continuum limit the Veneziano-Yankielowicz super-multiplet becomes massless and the Farrar-Gabadadze-Schwetz super-multiplet decouples from the theory. In addition, we estimate the masses of the excited mesons in the Veneziano-Yankielowicz multiplet. We observe that the gluino-glueballs have comparable masses to the excited mesons.

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Improved results forN=(2,2)super Yang-Mills theory using supersymmetric discrete light-cone quantization

Cited by 15 publications

References 30 publications

Dimensionally reduced SYM4 at large-N: an intriguing Coulomb approximation

Dimensionally reduced SYM4 at large-N: an intriguing Coulomb approximation

High precision study of the structure of supersymmetric Yang–Mills quantum mechanics

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

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