Topological structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>gluodynamics at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:math>: An analysis using the Symanzik action and Neuberger overlap fermions

Bornyakov, V. G.; Luschevskaya, E. V.; Morozov, S. M.; Polikarpov, M. I.; Ilgenfritz, Ernst-Michael; Müller–Preussker, M.

doi:10.1103/physrevd.79.054505

Cited by 28 publications

(41 citation statements)

References 30 publications

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“…In fact, in equilibrium configurations there is a small number of (exceptional) near-zero modes seen. This has been first discovered in [19] and recently confirmed in [12]. With increasing temperature, they become more and more separated from the rest of the spectrum (bulk) by the emerging gap and are decreasing in multiplicity [12].…”

Section: Overlap Fermion Spectramentioning

confidence: 96%

“…In this respect, the present work is a direct continuation of the previous one on calorons and dyons at the thermal phase transition [11]. The knowledge of the spectral density and localization properties of individual modes, now detailed for both signs of L for fixed, antiperiodic temporal boundary conditions [12] or -vice versa -depending on the temporal boundary conditions for fixed L > 0 as considered in this paper 1 , corroborates the interpretation of the present cluster results that has emerged in the meantime.…”

Section: Introductionmentioning

confidence: 93%

“…In Sect. III we discuss the reason for the enormous difference in localization [12] of the eigenmodes in the gap region between the two types of boundary conditions or between the two signs of the average Polyakov loop, respectively. In Sect.…”

Section: Introductionmentioning

confidence: 99%

“…Since that time, an extended and model-independent investigation of overlap fermion spectra for SU (2) below and above T c (up to T = 2 T c ) was performed [12]. The fermionic eigenmodes (and their spectral density) show some striking peculiarities above T c that our dyonic picture of the topological content of SU (2) lattice gauge theory seems to be able to explain.…”

Section: Introductionmentioning

confidence: 99%

“…II we analyze the properties of overlap fermion spectra above T c as found in this paper and in Ref. [12] on the basis of the dyonic picture of the topological content of SU (2) lattice gauge theory. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Dyonic picture of topological objects in the deconfined phase

et al. 2009

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In the deconfinement phase of quenched SU (2) Yang-Mills theory the spectrum and localization properties of the eigenmodes of the overlap Dirac operator with antiperiodic boundary conditions are strongly dependent on the sign of the average Polyakov loop, L . For L > 0 a gap appears with only few, highly localized topological zero and near-zero modes separated from the rest of the spectrum. Instead of a gap, for L < 0 a high spectral density of relatively delocalized near-zero modes is observed. In an ensemble of positive L , the same difference of the spectrum appears under a change of fermionic boundary conditions. We argue that this effect and other properties of near-zero modes can be explained through the asymmetric properties and the different abundance of dyons and antidyons -topological objects also known to appear, however in a symmetric form, in the confinement phase at T < Tc as constituents of calorons with maximally nontrivial holonomy.

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Section: Overlap Fermion Spectramentioning

confidence: 96%

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dyonic picture of topological objects in the deconfined phase

et al. 2009

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Inverse magnetic catalysis and the Polyakov loop

Bruckmann

Endrődi

Kovács

2013

J. High Energ. Phys.

292

315

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We study the physical mechanism of how an external magnetic field influences the QCD quark condensate. Two competing mechanisms are identified, both relying on the interaction between the magnetic field and the low quark modes. While the coupling to valence quarks enhances the condensate, the interaction with sea quarks suppresses it in the transition region. The latter `sea effect' acts by ordering the Polyakov loop and, thereby, reduces the number of small Dirac eigenmodes and the condensate. It is most effective around the transition temperature, where the Polyakov loop effective potential is flat and a small correction to it by the magnetic field can have a significant effect. Around the critical temperature, the sea suppression overwhelms the valence enhancement, resulting in a net suppression of the condensate, named inverse magnetic catalysis. We support this physical picture by lattice simulations including continuum extrapolated results on the Polyakov loop as a function of temperature and magnetic field. We argue that taking into account the increase in the Polyakov loop and its interaction with the low-lying modes is essential to obtain the full physical picture, and should be incorporated in effective models for the description of QCD in magnetic fields in the transition region.Comment: 19 pages, 8 figures, new reference added, version accepted for publicatio

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Symmetry crossover protecting chirality in Dirac spectra

Kanazawa

Kieburg

2018

J. High Energ. Phys.

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We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched partition functions. Some of these results have been announced in a former letter by us. Our derivation relies on the supersymmetry method and is performed here step by step. Additionally, we compute the chiral condensate and the pion condensate for the quenched as well as unquenched settings. We also investigate the limits to GUE and chGUE and confirm our conjecture that the non-uniformity of the GUE limit would carry over to the hard edge limit.

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Topological structure ofSU(2)gluodynamics atT>0: An analysis using the Symanzik action and Neuberger overlap fermions

Cited by 28 publications

References 30 publications

Dyonic picture of topological objects in the deconfined phase

Dyonic picture of topological objects in the deconfined phase

Inverse magnetic catalysis and the Polyakov loop

Symmetry crossover protecting chirality in Dirac spectra

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