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Overlap Dirac operator with chiral chemical potential and Chiral Magnetic Effect on the lattice
High Energy Physics - Lattice · Submitted 11 Sep 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that a straightforward lattice calculation with a constant magnetic field and a uniform chiral chemical potential in fact corresponds to an infrared singularity in the dimensionally reduced polarization tensor and hence yields the result which is extremely sensitive to infrared regulators such as finite volume or finite temperature.
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The abstract, sentence by sentence
A self-consistent construction of the overlap lattice Dirac operator coupled to chiral chemical potential is proposed. With the help of the constructed operator we compute electric current induced by a constant magnetic field (Chiral Magnetic Effect). We find that the result disagrees with the one predicted by anomaly-based arguments and comment on the origin of this discrepancy. We demonstrate that a straightforward lattice calculation with a constant magnetic field and a uniform chiral chemical potential in fact corresponds to an infrared singularity in the dimensionally reduced polarization tensor and hence yields the result which is extremely sensitive to infrared regulators such as finite volume or finite temperature.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A self-consistent construction of the overlap lattice Dirac operator coupled to chiral chemical potential is proposed. | contribution 0.78 | 0.91 | 0.06 | asserted 0.99 |
| s1 | With the help of the constructed operator we compute electric current induced by a constant magnetic field (Chiral Magnetic Effect). | contribution 0.56 | 0.95 | 0.07 | asserted 0.99 |
| s2 | We find that the result disagrees with the one predicted by anomaly-based arguments and comment on the origin of this discrepancy. | result 0.94 | 0.95 | 0.48 | asserted 1.00 |
| s3 | We demonstrate that a straightforward lattice calculation with a constant magnetic field and a uniform chiral chemical potential in fact corresponds to an infrared singularity in the dimensionally reduced polarization tensor and hence yields the result which is extremely sensitive to infrared regulators such as finite volume or finite temperature. | interpretation 0.88 | 0.91 | 0.64 | asserted 1.00 |
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The paper
Original abstract
A self-consistent construction of the overlap lattice Dirac operator coupled to chiral chemical potential is proposed. With the help of the constructed operator we compute electric current induced by a constant magnetic field (Chiral Magnetic Effect). We find that the result disagrees with the one predicted by anomaly-based arguments and comment on the origin of this discrepancy. We demonstrate that a straightforward lattice calculation with a constant magnetic field and a uniform chiral chemical potential in fact corresponds to an infrared singularity in the dimensionally reduced polarization tensor and hence yields the result which is extremely sensitive to infrared regulators such as finite volume or finite temperature.
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References
How the literature uses it
3 arXiv papers cite this in 6 sentences
What it cites · 13 sentences without a confident label
Builds on 2 papers
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In this work we construct the chiral lattice Dirac operator with finite chiral chemical potential $μ_5$ basing on the overlap Dirac operator at finite chemical potential [ref] and use it to calculate the CME current ([ref]) for free fermions in a constant magnetic field.
Overlap Dirac operator at nonzero chemical potential and random matrix theory · Introduction · 0.81
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In this work we construct the chiral lattice Dirac operator with finite chiral chemical potential $μ_5$ basing on the overlap Dirac operator at finite chemical potential [ref] and use it to calculate the CME current ([ref]) for free fermions in a constant magnetic field.
Exactly massless quarks on the lattice · Introduction · 0.81
Uses the method or tool of 2 papers
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The latter are coupled to fermions in a standard way by including the corresponding link factors into finite difference operators entering the Dirac-Wilson operator which is used to define the overlap Dirac operator [ref] .
Exactly massless quarks on the lattice · Overlap Dirac operator with chiral chemical potential · 0.93
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We now require that the variation ([ref]) is generated by an infinitesimal gauge transformation of the lattice axial gauge field $A_μx$: [equation] Expanding the right-hand side to the first order in $ax$ and comparing the result with the infinitesimal variation due to a gauge transformation of the vector gauge field [ref] , we obtain the following functional equation for $𝒟_ovV_μx, A_μx$: [equation] In order to solve this seemingly nonlinear equation, it is convenient to formulate it in terms of the projected overlap Dirac operator [equation] This transformation projects the eigenvalues of $𝒟_ov$ from the Ginsparg-Wilson circle in the complex plane to the imaginary axis.
Axial vector current of exact chiral symmetry on the lattice · Overlap Dirac operator with chiral chemical potential · 0.80
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