Coulomb gas and sine-Gordon model in arbitrary dimension

Nándori, I.

doi:10.1016/j.nuclphysb.2022.115681

Cited by 4 publications

(6 citation statements)

References 92 publications

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“…In [50] the wave function renormalization has both field-dependent and independent parts but the field-dependent part plays no important role in the phase structure (similarly to the higher harmonics of the potential), so, here we focus on the field-independent wave function renormalization. So let us summarize briefly the main results of [51] since our new results presented in the next section are based on that work. FRG flow equations for the Fourier amplitude and wave function renormalization are derived at LPA' level in [51] and read as follows ( )…”

Section: Non-perturbative Rg Flow Equations Of the Sg Model Taken At ...mentioning

confidence: 99%

“…So let us summarize briefly the main results of [51] since our new results presented in the next section are based on that work. FRG flow equations for the Fourier amplitude and wave function renormalization are derived at LPA' level in [51] and read as follows ( )…”

Section: Non-perturbative Rg Flow Equations Of the Sg Model Taken At ...mentioning

confidence: 99%

“…So, it can be seen as an RG scale-dependent wave function renormalization. The conclusion is that either one considers the Fourier amplitude and the wave function renormalization (u k , z k ) or the Fourier amplitude and the frequency b u , The FRG study of the SG model beyond LPA has been discussed in [34,50,51]. In [50] the wave function renormalization has both field-dependent and independent parts but the field-dependent part plays no important role in the phase structure (similarly to the higher harmonics of the potential), so, here we focus on the field-independent wave function renormalization.…”

Section: Non-perturbative Rg Flow Equations Of the Sg Model Taken At ...mentioning

confidence: 99%

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Perturbative versus non-perturbative renormalization

Hariharakrishnan,

Jentschura,

Márián

et al. 2024

J. Phys. G: Nucl. Part. Phys.

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Approximated functional renormalization group (FRG) equations lead to regulator-dependent beta-functions, in analogy to the scheme-dependence of the perturbative renormalization group (pRG) approach. A scheme transformation redefines the couplings to relate the beta-functions of the FRG method with an arbitrary regulator function to the pRG ones obtained in a given scheme. Here, we consider a periodic sine-Gordon scalar field theory in d=2 dimensions and show that the relation of the FRG and pRG approaches is intricate. Although, both the FRG and the pRG methods are known to be sufficient to obtain the critical frequency of the model independently of the choice of the regulator and the renormalization scheme, we show that one has to go beyond the standard pRG method (e.g., using an auxiliary mass term) or the Coulomb-gas representation in order to obtain the beta-function of the wave function renormalization. This aspect makes the scheme transformation non-trivial. Comparing flow equations of the two-dimensional sine-Gordon theory without any scheme-transformation, i.e., redefinition of couplings, we find that the auxiliary mass pRG beta-functions of the minimal subtraction scheme can be recovered within the FRG approach with the choice of the power-law regulator with b=2, therefore constitutes a preferred choice for the comparison of FRG and pRG flows.

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Section: Non-perturbative Rg Flow Equations Of the Sg Model Taken At ...mentioning

confidence: 99%

Section: Non-perturbative Rg Flow Equations Of the Sg Model Taken At ...mentioning

confidence: 99%

Section: Non-perturbative Rg Flow Equations Of the Sg Model Taken At ...mentioning

confidence: 99%

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Perturbative versus non-perturbative renormalization

Hariharakrishnan,

Jentschura,

Márián

et al. 2024

J. Phys. G: Nucl. Part. Phys.

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“…Another major example for non-differentiable potentials is coming from particle physics when the standard model quartic and quadratic Higgs potential is replaced by a periodic one, with the Higgs part given by the following Euclidean action [9,10]:…”

Section: Jhep07(2022)012mentioning

confidence: 99%

“…In the renormalization group (RG) point of view the phase structure has not been modified significantly if the Higgs potential remains polynomial. Instead, a periodic self-interaction, [9,10], potential but periodicity should be protected by the RG approach, so, no Taylor expansion can be applied. Thus, it is worthwhile to study the phase structure of a periodic potential defined by the following Euclidean action…”

Section: B Periodic Higgs Potentialmentioning

confidence: 99%

Renormalisation of non-differentiable potentials

Alexandre

Defenu

Grigolia

et al. 2022

J. High Energ. Phys.

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Non-differentiable potentials, such as the V-shaped (linear) potential, appear in various areas of physics. For example, the effective action for branons in the framework of the brane world scenario contains a Liouville-type interaction, i.e., an exponential of the V-shaped function. Another example is coming from particle physics when the standard model Higgs potential is replaced by a periodic self-interaction of an N-component scalar field which depends on the length, thus it is O(N) symmetric. We first compare classical and quantum dynamics near non-analytic points and discuss in this context the role of quantum fluctuations. We then study the renormalisation of such potentials, focusing on the Exact Wilsonian Renormalisation approach, and we discuss how quantum fluctuations smoothen the bare singularity of the potential. Applications of these results to the non-differentiable effective branon potential and to the O(N) models when the spatial dimension is varied and to the O(N) extension of the sine-Gordon model in (1+1) dimensions are presented.

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