QCD at small nonzero quark chemical potentials

Kogut, John B.; Toublan, D.

doi:10.1103/physrevd.64.034007

Cited by 147 publications

(259 citation statements)

References 24 publications

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“…In [4] this theory was studied in detail for N f = 3. It was found that a phase transition to a kaon condensed phase takes place at µ = M. For µ < M the saddle point of the static part of the effective Lagrangian is given by the identity matrix.…”

Section: Kaon Condensation In Qcdmentioning

confidence: 99%

“…For convenience, this quark will be identified as a strange quark. It is now well understood how to extend a chiral Lagrangian to nonzero chemical potential [20,18,3,2,4,19,21]: Requiring QCD and the low-energy effective Lagrangian to have the same transformation properties of a local external vector source uniquely determines the dependence of the chiral Lagrangian on this vector source and thus on the chemical potential. No additional parameters are necessary.…”

Section: Kaon Condensation In Qcdmentioning

confidence: 99%

“…(1) captures the essential physics of kaon condensation. Second, near the phase transition point, the low-energy limit of QCD at nonzero strangeness chemical potential given by the effective theory constructed in [4] can be reduced to the Lagrangian one involving only the strange degrees of freedom. The reason is that, at the phase transition point, only strange degrees of freedom become massless.…”

Section: Spectrum Of Goldstone Modes In a Simple Modelmentioning

confidence: 99%

“…For light quarks this phase transition takes place within the domain of validity of the chiral Lagrangian and is completely described by means of a low energy effective theory [2] which also describes phase quenched QCD [3]. Similarly, the low energy limit of QCD at at nonzero strange chemical potential, including its rich phase diagram at zero temperature can be completely described in terms of a chiral Lagrangian [4].…”

Section: Introductionmentioning

confidence: 99%

“…Goldstone's theorem will be discussed in section 3. In section 4 we analyze the low-energy limit of QCD at nonzero strangeness chemical potential which was constructed in [4]. Concluding remarks are made in section 5.…”

Section: Introductionmentioning

confidence: 99%

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Kaon condensation and Goldstone's theorem

et al. 2001

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We consider QCD at a nonzero chemical potential for strangeness. At a critical value of the chemical potential equal to the kaon mass, kaon condensation occurs through a continuous phase transition. We show that in the limit of exact isospin symmetry a Goldstone boson with the dispersion relation E ∼ p 2 appears in the kaon condensed phase. At the same time, the number of the Goldstone bosons is less than the number of broken generators. Both phenomena are familiar in non-relativistic systems. We interpret our results in terms of a Goldstone boson counting rule found previously by Nielsen and Chadha. We also formulate a criterion sufficient for the equality between the number of Goldstone bosons and the number of broken generators.

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Section: Kaon Condensation In Qcdmentioning

confidence: 99%

Section: Kaon Condensation In Qcdmentioning

confidence: 99%

Section: Spectrum Of Goldstone Modes In a Simple Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kaon condensation and Goldstone's theorem

et al. 2001

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Qcd, Chiral Random Matrix Theoryand Integrability

Verbaarschot

2006

NATO Science Series II: Mathematics, Physics and Chemistry

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SummaryRandom Matrix Theory has been a unifying approach in physics and mathematics. In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview of QCD, its low-energy limit and the microscopic limit of the Dirac spectrum which, as we will see in the second lecture, can be described by chiral Random Matrix Theory. The main topic of the third lecture is the recent developments on the relation between the QCD partition function and integrable hierarchies (in our case the Toda lattice hierarchy). This is an efficient way to obtain the QCD Dirac spectrum from the low energy limit of the QCD partition function. Finally, we will discuss the QCD Dirac spectrum at nonzero chemical potential. We will show that the microscopic spectral density is given by the replica limit of the Toda lattice equation. Recent results by Osborn on the Dirac spectrum of full QCD will be discussed.

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Pion and kaon condensation at zero temperature in three-flavor χPT at nonzero isospin and strange chemical potentials at next-to-leading order

Adhikari

Andersen

2020

J. High Energ. Phys.

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We consider three-flavor chiral perturbation theory (χPT) at zero temperature and nonzero isospin (µ I ) and strange (µ S ) chemical potentials. The effective potential is calculated to next-to-leading order (NLO) in the π ± -condensed phase, the K ± -condensed phase, and the K 0 /K 0 -condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, |µ, respectively at tree level and remains unchanged at NLO. The transition between the two condensed phases is first order. The effective potential in the pion-condensed phase is independent of µ S and in the kaon-condensed phases, it only depends on the combinations ± 1 2 µ I + µ S and not separately on µ I and µ S . We calculate the pressure, isospin density and the equation of state in the pion-condensed phase and compare our results with recent (2 + 1)-flavor lattice QCD data. We find that the threeflavor χPT results are in good agreement with lattice QCD for µ I < 200 MeV, however for larger values χPT produces values for observables that are consistently above lattice results. For µ I > 200 MeV, the two-flavor results are in better agreement with lattice data. Finally, we consider the observables in the limit of very heavy s-quark, where they reduce to their two-flavor counterparts with renormalized couplings. The disagreement between the predictions of two and three flavor χPT can largely be explained by the differences in the experimental values of the low-energy constants.

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QCD at small nonzero quark chemical potentials

Cited by 147 publications

References 24 publications

Kaon condensation and Goldstone's theorem

Kaon condensation and Goldstone's theorem

Qcd, Chiral Random Matrix Theoryand Integrability

Pion and kaon condensation at zero temperature in three-flavor χPT at nonzero isospin and strange chemical potentials at next-to-leading order

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