Asymptotic safety in the sine-Gordon model

Kovács, József; Nagy, S.; Sailer, K.

doi:10.1103/physrevd.91.045029

Cited by 6 publications

(4 citation statements)

References 79 publications

(103 reference statements)

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“…There are a large number of good reviews [8,9,10,11]. A lot of work has been done on the RG of the Sine-Gordon model over the last few years and many computations have been carried out analytically and numerically [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. This paper primarily studies the application of ERG mainly to two dimensional field theories -the emphasis being on a simple way of writing down the solution to the ERG in terms of an evolution operator.…”

Section: Introductionmentioning

confidence: 99%

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Exact renormalization group and Sine Gordon theory

Oak¹,

Sathiapalan²

2017

J. High Energ. Phys.

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Abstract:The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional φ 4 field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating cfunctions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact renormalization group and Sine Gordon theory

Oak¹,

Sathiapalan²

2017

J. High Energ. Phys.

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“…Interestingly the position of the Coleman point does not change [28]. There, the phase space can be completed by an IR and a UV non-Gaussian fixed points [33], althought there regimes are far from the physically interesting Coleman point, furthermore, the trajectories of the broken symmetric phase run into singularity, i.e. ũ → −1 in the IR limit.…”

Section: The Local Sine-gordon Modelmentioning

confidence: 96%

Renormalization of the bilocal sine-Gordon model

Steib

Nagy

2019

Int. J. Mod. Phys. A

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The functional renormalization group treatment is presented for the twodimensional sine-Gordon model by including a bilocal term in the potential, which contributes to the flow at tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, and then the Kosterlitz-Thouless type phase transition can be recovered. I. INTRODUCTIONThe quantum field theoretical models suffer from ultraviolet (UV) divergences, and we should remove the infinities by regularizations. They imply that we should consider an effective dynamics of the models, where certain degrees of freedom or modes of the physical system are not followed, they do not belong to the system anymore, they are pushed to the environment. However, if we integrate out certain degrees of freedom, then the remaining effective model of the system modes becomes nonlocal [1]. Earlier works investigated nonlocal field theories at perturbative level [2,3]. Nevertheless, the theories including nonlocal interactions have to face with the violation of causality [4-6], instability problems [7,8], or the spoiling of gauge invariance [9][10][11].The introduction of a momentum cutoff, as a simple regularization, also leads to nonlocal interactions. The same problem takes place, when we use the functional renormalization group (RG) method [12][13][14][15][16]. Recently it has been pointed out, that RG blocking step introduces nonlocal contributions to the evolution [17][18][19]. During the blocking some ultraviolet (UV) modes in the momentum shell are integrated out, transforming system degrees of freedom into the environmental ones. The nonlocality has not been followed during the traditional the RG method, because we usually use local actions and do not let the nonlocal terms to evolve. However there is a nontrivial saddle point for the integrated UV modes, which introduces a nonlocal term, moreover it contributes to the RG evolution at tree level.

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“…There is BKT physics in the SG model, so it is widely applied and compared in the 2D XY models. [20] There are nontrivial fixed points in the IR limit, which showed them an irrelevant coupling leads to the same phase structure. Nonconservative kinks shown at the continuum limit with unusual divergence and conventional Kousterlitz-Thoules point consist of normal behavior as that of the Coleman point, which can be anomalous [21].…”

Section: Introductionmentioning

confidence: 98%

Derivation of $\mathcal{PT}$-symmetric Sine-Gordon model and its relevance to non-equilibrium

Kulkarni¹

2022

Preprint

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The Parity-Time PT -symmetric non-Hermitian Sine-Gordon(nhSG) model derived from the nonequilibrium spin-boson model. We have derived the Keldysh rotation for spin operators, from which the SG model can be derived. We perform renormalization group calculations in the Keldysh fields and compare the fixed points and the flow of the effective couplings of nonequilibrium and non-Hermitian models. Also, we explicitly find the self-energies and compare the two methods to understand the regimes where PT symmetry preserved regime, and nonequilibrium regimes persist.RG flow of couplings of nonequilibrium model and non-hermitian model both capture the standard Berezinskii-Kosterlitz-Thouless(BKT) physics in a strong coupling regime.

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Asymptotic safety in the sine-Gordon model

Cited by 6 publications

References 79 publications

Exact renormalization group and Sine Gordon theory

Exact renormalization group and Sine Gordon theory

Renormalization of the bilocal sine-Gordon model

Derivation of $\mathcal{PT}$-symmetric Sine-Gordon model and its relevance to non-equilibrium

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