Computation of the one-loop Symanzik coefficients for the square action

Snippe, Jeroen

doi:10.1016/s0550-3213(97)00270-8

Cited by 29 publications

(67 citation statements)

References 46 publications

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“…In this case the plaquette definition approximates the continuum result much better than the symmetric one. For comparison we also display in figure 1(c) the results that are obtained if the Symanzik improved Square action [20,21] is used for the flow (details are given in appendix A).…”

Section: Jhep01(2015)038mentioning

confidence: 99%

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The SU(∞) twisted gradient flow running coupling

Pérez

González-Arroyo

Keegan

et al. 2015

J. High Energ. Phys.

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Abstract:We measure the running of the SU(∞) 't Hooft coupling by performing a step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU(N ) gauge theory on a single site lattice with twisted boundary conditions. The computation relies on the conjecture that finite volume effects for SU(N) gauge theories defined on a 4-dimensional twisted torus are controlled by an effective size parameterl = l √ N , with l the torus period. We set the scale for the running coupling in terms ofl and use the gradient flow to define a renormalized 't Hooft coupling λ(l). In the TEK model, this idea allows the determination of the running of the coupling through a step scaling procedure that uses the rank of the group as a size parameter. The continuum renormalized coupling constant is extracted in the zero lattice spacing limit, which in the TEK model corresponds to the large N limit taken at fixed value of λ(l). The coupling constant is thus expected to coincide with that of the ordinary pure gauge theory at N = ∞. The idea is shown to work and permits us to follow the evolution of the coupling over a wide range of scales. At weak coupling we find a remarkable agreement with the perturbative two-loop formula for the running coupling.

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Section: Jhep01(2015)038mentioning

confidence: 99%

“…We have considered in particular the Symanzik improved Square action [20,21] which combines 1 × 1, 1 × 2 and 2 × 2 plaquettes:…”

Section: Jhep01(2015)038mentioning

confidence: 99%

The SU(∞) twisted gradient flow running coupling

Pérez

González-Arroyo

Keegan

et al. 2015

J. High Energ. Phys.

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“…In the following, we will employ twisted boundary conditions [23] in much the same way as in [10,11]. The twisted boundary conditions we use for gluons and quarks are applied to the (x, y) directions and are given by (ν = x, y)…”

Section: Twisted Boundary Conditionsmentioning

confidence: 99%

“…(11). In particular, this removes the zero mode from the gluon spectrum and so the mass-scale m defined above acts as a gauge-invariant infra-red regulator.…”

Section: Twisted Boundary Conditionsmentioning

confidence: 99%

“…The twisted theory can be viewed as a two-dimensional field theory in the infinite (z, t) plane with the modes in the twisted directions being considered in the spirit of Kaluza-Klein modes. Denoting n = (n x , n y ), the stable particles in the (z, t) continuum limit of this effective theory are called the A mesons (n = (1, 0) or n = (0, 1)) with mass m and the B mesons (n = (1, 1)) with mass √ 2m [11].…”

Section: Twisted Boundary Conditionsmentioning

confidence: 99%

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Unquenching effects on the coefficients of the Lüscher-Weisz action

et al. 2007

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The twisted gradient flow coupling at one loop

Bribian

Pérez

2019

J. High Energ. Phys.

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We compute the one-loop running of the SU (N ) 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scalel given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the MS scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of Λ parameters between the two schemes. We analyze the N dependence of the results and the possible implications for non-commutative gauge theories and volume independence.

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Computation of the one-loop Symanzik coefficients for the square action

Cited by 29 publications

References 46 publications

The SU(∞) twisted gradient flow running coupling

The SU(∞) twisted gradient flow running coupling

Unquenching effects on the coefficients of the Lüscher-Weisz action

The twisted gradient flow coupling at one loop

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