Son-Yamamoto relation and holographic renormalization group flows

Dubinkin, Oleg; Gorsky, A.; Milekhin, Alexey

doi:10.1103/physrevd.91.066007

Cited by 3 publications

(6 citation statements)

References 25 publications

(30 reference statements)

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“…Hence we could question when the jump of chiral conductivity is expected in the holographic setup. To be as model independent as possible consider the anomaly matching Son-Yamamoto condition in holographic QCD [37] which yields the relation between the 2-and 3-point functions and is diagonal with respect to the holographic RG flows in the hard wall model [38]. The Son-Yamamoto relation amounts to the following expression for the "running"F π…”

Section: Spectral Statistics In the Deconfined Phase A Field Theory A...mentioning

confidence: 99%

Metal or insulator? Dirac operator spectrum in holographic QCD

Gorsky

Litvinov

2019

Physics Letters B

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The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of 4 + 1 dimensional disordered system. We use the holographic viewpoint to provide the conjectural explanation of these properties. The delocalization of all modes in the confined phase is related to the θ = π -like phenomena when the fermions are delocalized on domain walls. It is conjectured that the localized modes separated by mobility edge from the rest of the spectrum in deconfined QCD correspond to the near-horizon region in the holographic dual. arXiv:1812.02321v2 [hep-th] 2 Jul 2019Wigner-Dyson statistics, while the localized modes do not interact at all and obey the Poisson statistics. There can be a mobility edge separating localized and delocalized modes in the d ≥ 3, where d is dimension of space. In 1 + 1 and 2 + 1 dimensions the most of modes are localized, however, there could be a few delocalized modes if the topological terms are present in the action [7][8][9][10]. For instance, these distinguished delocalized modes are responsible for the Hall conductivity in 2 + 1 case.The properties of the Dirac operator spectrum have been investigated in the lattice QCD and the results found were a bit surprising. They can be summarized as follows:• All modes are delocalized in the confined phase [11] • There is the mobility edge λ m in the deconfined phase [11,13]. Low energy modes in the deconfined phase are localized while high energy part of the spectrum is delocalized. • The mobility edge λ m (T ) at T > T c grows as the function of the temperature near the deconfinement phase transition approximately as [12] λ m (T ) = a(T − T c ) with come constant a. The fractal dimension at the localization phase transition coincides with the fractal dimension of 3D unitary Anderson model [14].

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Section: Spectral Statistics In the Deconfined Phase A Field Theory A...mentioning

confidence: 99%

Metal or insulator? Dirac operator spectrum in holographic QCD

Gorsky

Litvinov

2019

Physics Letters B

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“…(34) to be equal to 4πκ = N c ) is the perturbative contribution of the axial anomaly, which is obtained from PT loop calculation. In QCD, the integral of the metric factor 1/f 2 produces 1/f 2 π where f π is the pion decay constant [11]. We rewrite the Son-Yamamoto relation in the form…”

Section: Mixed Correlatormentioning

confidence: 99%

“…(6) enable us to simplify the holographic action. As discussed in [11], in the Yang-Mills action, we can neglect ∂ z V µ = 0, however we approximate ∂ z A µ = Aµ z0 . Therefore we can write to the leading order…”

Section: Regime Of Small Qmentioning

confidence: 99%

“…In this section we draw parallels between the 4-dimensional QCD [1], [11] and our 2-dimensional system. We write formulas for the 2D system in the context of QCD 2 .…”

Section: Similarity Of Qcd and Two-dimensional System Dimensionalmentioning

confidence: 99%

“…The second approach provides correct results for anomalies and gives a simple description of RF flow in deformed CFT's [10]. We apply Hamilton-Jacobi equation in the bulk theory to the Yang-Mills-Chern-Simons holographic action similar to [11] and demonstrate that SY relation is diagonal with respect to holographic RG flow. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Anomaly matching condition in two-dimensional systems

2016

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Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in QCD 4 , we derive its analog in two-dimensional system. It connects the transverse part of mixed vector-axial current two-point function with diagonal vector and axial current two-point functions.Being fully non-perturbative, this relation may be regarded as anomaly matching for conductivities or certain transport coefficients depending on the system. We consider the holographic RG flows in holographic Yang-Mills-Chern-Simons theory via the Hamilton-Jacobi equation with respect to the radial coordinate. Within this holographic model it is found that the RG flows for the following relations are diagonal: Son-Yamamoto relation and the left-right polarization operator. Thus the Son-Yamamoto relation holds at wide range of energy scales.

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Mobility edge and Black Hole Horizon

Gorsky

2018

EPJ Web Conf.

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Son-Yamamoto relation and holographic renormalization group flows

Cited by 3 publications

References 25 publications

Metal or insulator? Dirac operator spectrum in holographic QCD

Metal or insulator? Dirac operator spectrum in holographic QCD

Anomaly matching condition in two-dimensional systems

Mobility edge and Black Hole Horizon

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