Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models

Pérez, Margarita Garcı́a; González-Arroyo, Antonio; Okawa, M.

doi:10.1007/jhep10(2017)150

Cited by 15 publications

(11 citation statements)

References 81 publications

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“…Although our new condition has been obtained for the 2+1 dimensional system it might also affect the 4 dimensional case, but replacing N by √ N . Indeed, it can be shown that the value of Z min controls the size of the contribution of non-planar diagrams in perturbation theory [40]. However, if that also affects the existence of symmetry-breaking phase transitions in the non-perturbative region of the 3+1 system would only show up for N = 44 2 = 1936 or higher, which is hard to check.…”

Section: Conditions On the Flux For The Absence Of Phase Transitionsmentioning

confidence: 99%

The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

Pérez

González-Arroyo

Koren

et al. 2018

J. High Energ. Phys.

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We compute and analyse the low-lying spectrum of 2+1 dimensional SU(N ) Yang-Mills theory on a spatial torus of size l × l with twisted boundary conditions. This paper extends our previous work [1]. In that paper we studied the sector with non-vanishing electric flux and concluded that the energies only depend on the parameters through two combinations: x = λN l/(4π) (with λ the 't Hooft coupling) and the twist angleθ defined in terms of the magnetic flux piercing the two-dimensional box. Here we made a more complete study and we are able to condense our results, obtained by non-perturbative lattice methods, into a simple expression which has important implications for the absence of tachyonic instabilities, volume independence and non-commutative field theory. Then we extend our study to the sector of vanishing electric flux. We conclude that the onset of the would-be large-volume glueball states occurs at an approximately fixed value of x, much before the stringy torelon states have become very massive.

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Section: Conditions On the Flux For The Absence Of Phase Transitionsmentioning

confidence: 99%

The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

Pérez

González-Arroyo

Koren

et al. 2018

J. High Energ. Phys.

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“…The general procedure is similar to the infinite volume one in [3], though the computations and regularisation procedure turn out to be quite different. We first rescale the gauge fields in the Lagrangian, A µ (x) → g 0 A µ (x), and determine the Feynman rules in momentum space, which are essentially the usual ones replacing the group structure constants with F(p, q, −p − q); see for instance [18] and [19] for an analogous perturbative computation on the lattice. We then expand the flowed fields in powers of the bare coupling:…”

Section: Lo and Nlo Terms In Perturbation Theorymentioning

confidence: 99%

The perturbative SU(N) one-loop running coupling in the twisted gradient flow scheme

Bribian¹,

Pérez²

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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“…While we have chosen these two particular examples for illustration purposes, the appearance of spikes is a general phenomenon that we observe for orders approximately ≥ 30 on the volumes under study. is volume independent [48]. The infinite-volume value of p 1 can be obtained adding to the pure gauge contribution [49],…”

Section: Determination Of the P Nmentioning

confidence: 99%

“…Recently, the computation of Wilson loops has been treated in detail in Ref. [48]. Here we focus on two vertices, introducing Wilson and staggered fermions with smell in the fundamental representation.…”

Section: A Group Theory Conventionsmentioning

confidence: 99%

Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD

2018

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Numerical Stochastic Perturbation Theory (NSPT) allows for perturbative computations in quantum field theory. We present an implementation of NSPT that yields results for high orders in the perturbative expansion of lattice gauge theories coupled to fermions. The zero-momentum mode is removed by imposing twisted boundary conditions; in turn, twisted boundary conditions require us to introduce a smell degree of freedom in order to include fermions in the fundamental representation. As a first application, we compute the critical mass of two flavours of Wilson fermions up to order in a gauge theory. We also implement, for the first time, staggered fermions in NSPT. The residual chiral symmetry of staggered fermions protects the theory from an additive mass renormalisation. We compute the perturbative expansion of the plaquette with two flavours of massless staggered fermions up to order in a gauge theory, and investigate the renormalon behaviour of such series. We are able to subtract the power divergence in the Operator Product Expansion (OPE) for the plaquette and estimate the gluon condensate in massless QCD. Our results confirm that NSPT provides a viable way to probe systematically the asymptotic behaviour of perturbative series in QCD and, eventually, gauge theories with fermions in higher representations.

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Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models

Cited by 15 publications

References 81 publications

The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

The perturbative SU(N) one-loop running coupling in the twisted gradient flow scheme

Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD

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