<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">SU</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>gauge theories in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>dimensions: Further results

We present a numerical study of the lattice Landau gluon and ghost propagators in three-dimensional pure SU (2) gauge theory. Data have been obtained using asymmetric lattices (V = 20 2 ×60, 40 2 ×60, 8 2 × 64, 8 2 × 140, 12 2 × 140 and 16 2 × 140) for the lattice coupling β = 3.4, in the scaling region. We find that the gluon (respectively ghost) propagator is suppressed (respec. enhanced) at small momenta in the limit of large lattice volume V . By comparing these results with data obtained using symmetric lattices (V = 60 3 and 140 3 ), we find that both propagators suffer from systematic effects in the infrared region (p 650MeV). In particular, the gluon (respec. ghost) propagator is less IR-suppressed (respec. enhanced) than in the symmetric case. We discuss possible implications of the use of asymmetric lattices.

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“…2 and Table IV of Ref. [48]. This gives √ σ = 0.506(5), implying a lattice spacing a = 0.227(2) fm, i.e.…”

Section: Simulationsmentioning

confidence: 98%

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Cucchieri

Mendes

2006

Phys. Rev. D

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“…These expectations are largely based on an analysis of all-orders perturbation theory, so it is interesting to ask how precisely they are confirmed by non-perturbative lattice calculations. This question has been addressed in the past [53,59,60], but here we can go somewhat further using the very precise string tensions calculated for N ∈ [2,8] in [22]. We display in figure 1 the continuum values of √ σ/g 2 N taken from the first row of table 2 in [22].…”

Section: Large-n Limitmentioning

confidence: 99%

“…(In actual fact the correction is so small that its particular form is not important to the extracted value of a 2 σ.) The mass gap comes from [53,59,60] and the critical length from calculations of the D = 2 + 1 deconfining temperature in [10][11][12][13]. In table 6 we do the same for the SU(2) and SU(4) calculations that are dedicated to calculating the ground state.…”

mentioning

confidence: 99%

Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

Athenodorou

Bringoltz²,

Teper

2011

J. High Energ. Phys.

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We carry out lattice calculations of the spectrum of confining flux tubes that wind around a spatial torus of variable length l, in 2+1 dimensions. We compare the energies of the lowest ∼ 30 states to the free string Nambu-Goto model and to recent results on the universal properties of effective string actions. Our most useful calculations are in SU(6) at a small lattice spacing, which we check is very close to the N → ∞ continuum limit. We find that the energies, E n (l), are remarkably close to the predictions of the free string Nambu-Goto model, even well below the critical length at which the expansion of the Nambu-Goto energy in powers of 1/l 2 diverges and the series needs to be resummed. Our analysis of the ground state supports the universality of the O(1/l) and the O(1/l 3 ) corrections to σl, and we find that the deviations from Nambu-Goto at small l prefer a leading correction that is O(1/l 7 ), consistent with theoretical expectations. We find that the low-lying states that contain a single phonon excitation are also consistent with the leading O(1/l 7 ) correction dominating down to the smallest values of l. By contrast our analysis of the other light excited states clearly shows that for these states the corrections at smaller l resum to a much smaller effective power. Finally, and in contrast to our recent calculations in D = 3 + 1, we find no evidence for the presence of any non-stringy states that could indicate the excitation of massive flux tube modes.

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“…In fact our calculations are accurate enough to confirm the presence of the additional zero-point energy, as discussed in Section 4.2 and displayed in Fig.4. Indeed we saw that in any non-stringy attempt to describe these spectra, the particle excitation carrying the non-zero momentum will have a mass that is constrained by our calculated spectrum to be very much smaller than the known mass gap of the bulk space-time theory [23,24]. Thus such a (presumably massless) excitation must exist on the flux tube rather than in the bulk, and will thus arise from an effective string action.…”

Section: Discussionmentioning

confidence: 99%

“…Roughly speaking this tells us that m 2 /σ 2a 0.1 (1). This is to be compared to the known value of the mass gap in the SU(6) gauge theory [23,24] which is m 2 G /σ 2a ∼ 13. Thus this 'particle' cannot be an excitation in the bulk space-time, and must be an excitation that lives on the flux tube.…”

Section: K=2a 2smentioning

confidence: 99%

Closed flux tubes in higher representations and their string description in D=2+1 SU(N) gauge theories

Athenodorou

Teper²

2013

J. High Energ. Phys.

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We calculate, numerically, the low-lying spectrum of closed confining flux tubes that carry flux in different representations of SU(N). We do so for SU(6) at β = 171, where the calculated low-energy physics is very close to the continuum limit and, in many respects, also close to N = ∞. We focus on the adjoint, 84, 120, k = 2A, 2S and k = 3A, 3M, 3S representations and provide evidence that the corresponding flux tubes, albeit mostly unstable, do in fact exist. We observe that the ground state of a flux tube with momentum along its axis appears to be well defined in all cases and is well described by the Nambu-Goto free string spectrum, all the way down to very small lengths, just as it is for flux tubes carrying fundamental flux. Excited states, however, typically show very much larger deviations from Nambu-Goto than the corresponding excitations of fundamental flux tubes and, indeed, cannot be extracted in many cases. We discuss whether what we are seeing here are separate stringy and massive modes or simply large corrections to energy levels that will become string-like at larger lengths.

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SU(N)gauge theories in2+1dimensions: Further results

Cited by 91 publications

References 16 publications

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

Closed flux tubes in higher representations and their string description in D=2+1 SU(N) gauge theories

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