Localization transition in SU(3) gauge theory

Kovács, Tamás; Vig, Reka A.

doi:10.1103/physrevd.97.014502

Cited by 38 publications

(64 citation statements)

References 26 publications

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Section: Contentssupporting

confidence: 71%

“…The mobility edge, λ c , vanishes at a temperature compatible with T c [16], suggesting that localisation of the low Dirac modes is closely related to deconfinement and chiral restoration. This is further supported by a similar coincidence of the three phenomena in other theories and models, like SU(3) pure gauge theory in 3+1 dimensions [22], the N f = 3 unimproved staggered fermion model mentioned above [23], and also in a toy model for QCD [24], devised in Ref.[25] precisely to study the issue of localisation.A qualitative understanding of the relation between deconfinement and localisation is provided by what in this paper will be referred to as the "sea/islands" picture of localisation [26,27]. The idea is that the local Polyakov lines provide a sort of local potential for the Dirac modes via the effective boundary condition that they impose on the eigenmodes.…”

supporting

confidence: 63%

“…Localisation in the high-temperature, deconfined phase has been observed also in other gauge theories (see Ref. [36] for a recent review), namely SU(2) [15] and SU(3) pure gauge theory [22], and SU(3) with N f = 3 flavours of unimproved rooted staggered fermions on N t = 4 lattices [23]. In these models the finite-temperature transition is a genuine phase transition, which provides a clean-cut setting for investigating the possible coincidence of deconfinement, chiral-symmetry restoration and localisation of the low Dirac modes.…”

Section: Localisation In Lattice Gauge Theoriesmentioning

confidence: 73%

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Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Giordano

2019

J. High Energ. Phys.

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I study the localisation properties of low Dirac eigenmodes in 2+1 dimensional SU(3) pure gauge theory, both in the low-temperature, confined and chirally-broken phase and in the high-temperature, deconfined and chirally-restored phase, by means of numerical lattice simulations. While these modes are delocalised at low temperature, they become localised at high temperature, up to a critical point in the Dirac spectrum where a BKT-type Anderson transition takes place. All results point to localisation appearing at the deconfinement temperature, and support previous expectations about the close relation between deconfinement, chiral symmetry breaking, and localisation. Contents1 Introduction 1 2 Localisation in lattice gauge theories 4 3 Lattice SU(3) pure gauge theory in 2+1 dimensions 7 4 Numerical results 9 4.1 Participation ratio 10 4.2 Spectral statistics 16 5 Conclusions and outlook 28with N f = 2 flavours of adjoint fermions [9] on the lattice: 2 here two phase transitions are present, a deconfining one at T dec and a chiral-symmetry-restoring one at T χ with T dec < T χ . Nonetheless, at T dec the chiral condensate jumps downwards, and a partial restoration of chiral symmetry happens via a first-order phase transition. It is also well known that the fate of chiral symmetry is determined by the spectrum of the Dirac operator near the origin. In fact, the celebrated Banks-Casher relation [11] establishes that the chiral condensate in the chiral limit is proportional to the spectral density of the Dirac operator near the origin. For finite but small quark masses, an accumulation of eigenmodes near the origin is still expected at low temperatures, leading to light pions and all the other phenomenological consequences for QCD due to its being close to a theory with spontaneously broken symmetry. At high temperatures, instead, the spectral density is expected to vanish near the origin, reflecting the restoration of chiral symmetry in the massless case. Given the close relation between confining and chiral properties of the theory, it is natural to wonder if confinement is somehow responsible for the accumulation of modes near the origin, and analogously if deconfinement causes the depletion of this spectral region. A similar question of course can be asked also for other gauge theories.Adding to the mistery, or possibly helping to solve it, a third phenomenon has been observed to take place in QCD around the critical temperature, namely the localisation of the lowest modes of the Dirac operator [12][13][14][15][16][17][18]. Numerical studies on the lattice have shown that while in the low-temperature phase all the Dirac modes are extended throughout the whole system, above T c the lowest modes get localised [12][13][14][15][16][17][18] on the scale of the inverse temperature [16]. More precisely, modes are localised up to a temperature-dependent critical point in the spectrum, λ c = λ c (T ). 3 At λ c , a second-order phase transition takes place in the spectrum [19], and modes become delocalised. This type of tr...

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Section: Contentssupporting

confidence: 71%

supporting

confidence: 63%

Section: Localisation In Lattice Gauge Theoriesmentioning

confidence: 73%

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Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Giordano

2019

J. High Energ. Phys.

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“…Indeed, the bimodality in ρ(λ) was first observed with overlap operator that fully respects chirality, while it was not seen by the staggered operator on identical backgrounds [19]. However, the IR peak has recently been identified by staggered-type operator in pgQCD on larger volumes [26], confirming that the presence of this feature is discretization independent. This is also consistent with bimodality of the overlap operator persisting into the continuum limit, shown in Ref.…”

Section: Synthesis and Main Pointsmentioning

confidence: 88%

Possible new phase of thermal QCD

Alexandru

Horváth

2019

Phys. Rev. D

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Using lattice simulations, we show that there is a phase of thermal QCD, where the spectral density ρ(λ) of Dirac operator changes as 1/λ for infrared eigenvalues λ < T .This behavior persists over the entire low energy band we can resolve accurately, over three orders of magnitude on our largest volumes. We propose that in this "IR phase", the well-known non-interacting scale invariance at very short distances (UV, λ → ∞, asymptotic freedom), coexists with very different interacting type of scale invariance at long distances (IR, λ < T ). Such dynamics may be responsible for the unusual fluidity properties of the medium observed at RHIC and LHC. We point out its connection to the physics of Banks-Zaks fixed point, leading to the possibility of massless glueballs in the fluid. Our results lead to the classification of thermal QCD phases in terms of IR scale invariance. The ensuing picture naturally subsumes the standard chiral crossover feature at "T c " ≈ 155 MeV. Its crucial new aspect is the existence of temperature T IR (200 MeV < T IR < 250 MeV) marking the onset of IR phase and possibly a true phase transition. arXiv:1906.08047v1 [hep-lat] 17 Jun 2019 1. Introduction. The study of strongly interacting matter as a function of temperature and baryon density is an active area of theoretical and experimental research (see [1] for recent review). At high energies of colliding heavy nuclei, such as those studied at LHC and the high end of RHIC, baryon densities are small enough so that the results are generally expected, among other things, to shed light on the nature and properties of thermal QCD transition in the early universe. In this regime, it has become widely accepted, largely due to the matured power of lattice QCD [2], that increasing temperature leads to a smooth crossover in properties of thermal strongly interacting matter. On the experimental side, results from RHIC [3-6] and LHC [7] based on modeling the time evolution of collisions in terms of relativistic hydrodynamics, produced a picture of strongly coupled liquid-like medium with extremely low η/s (shear viscosity/entropy density) at high temperatures. In parallel and initially independent developments, similar values of η/s were obtained in highly symmetric and strongly coupled gauge theories with large number of colors, studied by means of their holographic dual [8]. This sparked a flurry of attempts to model the medium seen in the experiments via more refined descriptions of this type.However, the physics of thermal QCD transition(s) and the nature of the discovered liquid-like state of matter are far from settled, even in the limit of vanishing net baryon density (µ = 0), the setting of our interest. Among other things, the currently favored scenario involving a single feature (crossover at"T c ") offers limited room for accommodating a dramatic change from medium described as weakly interacting hadron resonance gas to strongly interacting near-perfect fluid. In this work, we propose a hierarchy of thermal effects in QCD, based on scale inv...

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“…Localized modes at the low end of the spectrum can be easily distinguished from the higher, delocalized part of the spectrum by tracing how the spectral statistics changes along the spectrum. For a detailed account of the determination of the mobility edge, separating localized and delocalized modes, see the contribution by R. A. Vig at this conference and also [10]. We can then count the average number of eigenvalues below the mobility edge and compare that to the number of eigenvalues in the zero mode zone to see whether the zero mode zone can account for localization.…”

Section: Pos(lattice2018)258mentioning

confidence: 99%

Localization and topology in high temperature QCD

Kovács

Vig

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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At high temperature part of the spectrum of the quark Dirac operator is known to consist of localized states. This comes about because around the crossover temperature to the quark-gluon plasma localized states start to appear at the low end of the spectrum and as the system is further heated, states higher up in the spectrum also get localized. Since localization and the crossover to the chirally restored phase happen around the same temperature, the question of how the two phenomena are connected naturally arises. Here we speculate on the nature of possible gauge configurations that could support localized quark eigenmodes. In particular, by analyzing eigenmodes of the staggerd and overlap Dirac operator we show that the dilute gas of calorons in the high temperature phase is very unlikely to play a major role in localization.

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Localization transition in SU(3) gauge theory

Cited by 38 publications

References 26 publications

Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Possible new phase of thermal QCD

Localization and topology in high temperature QCD

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