A quark-antiquark condensate in three-dimensional QCD

Damgaard, Poul H.; Heller, Urs M.; Krasnitz, A.; Madsen, T.

doi:10.1016/s0370-2693(98)01073-9

Cited by 32 publications

(54 citation statements)

References 24 publications

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“…For an odd number of flavors it has been argued that the pattern of spontaneous symmetry breaking pattern is replaced by U (2N f +1) → U (N f +1)×U (N f ) [2]. This picture of spontaneous flavor symmetry breaking has been supported by recent Monte Carlo simulations [3].…”

Section: Introductionsupporting

confidence: 50%

“…First, in section 5, a small-mass series expansion of the resolvent of the QCD 3 Dirac operator is generated by means of Virasoro constraints on the finite volume QCD 3 partition function. As a by-product of this analysis we derive a series of spectral sum rules for the Dirac operator in QCD 3 . In section 6, we explore the (large-mass) saddle-point expansion of the resolvent, which turns out to truncate after a finite number of terms, and hence is exact.…”

Section: Introductionmentioning

confidence: 99%

“…In ref. [2] the low-energy effective partition function of the corresponding chiral Lagrangian was used to extract information on the spectrum of the Dirac operator of QCD 3 . It was also suggested [2] that Random Matrix Theory may be used to exactly compute the microscopic properties of the Dirac spectrum in much the same way as was first proposed for QCD in 3+1 dimensions (QCD 4 ) [4].…”

Section: Introductionmentioning

confidence: 99%

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QCD3 and the replica method

Akemann

Dalmazi

Damgaard³

et al. 2001

Nuclear Physics B

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Using the replica method, we analyze the mass dependence of the QCD 3 partition function in a parameter range where the leading contribution is from the zero momentum Goldstone fields. Three complementary approaches are considered in this article. First, we derive exact relations between the QCD 3 partition function and the QCD 4 partition function continued to half-integer topological charge. The replica limit of these formulas results in exact relations between the corresponding microscopic spectral densities of QCD 3 and QCD 4 . Replica calculations, which are exact for QCD 4 at half-integer topological charge, thus result in exact expressions for the microscopic spectral density of the QCD 3 Dirac operator. Second, we derive Virasoro constraints for the QCD 3 partition function. They uniquely determine the small-mass expansion of the partition function and the corresponding sum rules for inverse Dirac eigenvalues. Due to de Wit-'t Hooft poles, the replica limit only reproduces the small mass expansion of the resolvent up to a finite number of terms. Third, the large mass expansion of the resolvent is obtained from the replica limit of a loop expansion of the QCD 3 partition function. Because of Duistermaat-Heckman localization exact results are obtained for the microscopic spectral density in this way.

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Section: Introductionsupporting

confidence: 50%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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QCD3 and the replica method

Akemann

Dalmazi

Damgaard³

et al. 2001

Nuclear Physics B

Self Cite

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“…Evidence for such a symmetry breaking pattern has been observed in 3D lattice simulations [18] with gauge group SU(3). This pattern of flavor symmetry breaking can also be predicted for 3D QCD at large N C using the ColemanWitten argument [19].…”

Section: Introductionmentioning

confidence: 86%

3D two-color QCD at finite temperature and baryon density

Dunne

Nishigaki

2003

Nuclear Physics B

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We study the phase diagram for two-color QCD in three-dimensional spacetime, as a function of temperature and baryon chemical potential, using the low-energy effective Lagrangian approach. We show one-loop renormalizability at zero temperature, and then use the one-loop effective Lagrangian at finite temperature and chemical potential to show that at low temperature there is a critical line separating the normal and diquark phase, with this critical line ending at a tricritical point. This phase structure is qualitatively similar to that found recently by Splittorff et al. for two-color QCD in four-dimensional spacetime, although the details are quite different, due to the different symmetries and the different loop and infrared properties of three-dimensional spacetime.

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“…Actually some tests have been done in the past but they were not conclusive [7]. In this work we repeat quenched simulations of lattice QCD 3 lattice to the chiral random matrix prediction (blue dotted line) and the corresponding non-chiral random matrix prediction (green solid line).…”

Section: Introductionmentioning

confidence: 99%

Random matrix model forQCD3staggered fermions

2011

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We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD3 at small lattice coupling constant β has exactly the same shape as in QCD4. This observation is quite surprising, since universal properties of the QCD3 Dirac operator are expected to be described by a non-chiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves towards the non-chiral random matrix prediction when β is increased and the continuum limit is approached. We propose a two-matrix model with one free parameter which interpolates between the two limits and very well mimics the pattern of evolution with β of the eigenvalue density of the staggered fermion operator in QCD3.

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A quark-antiquark condensate in three-dimensional QCD

Cited by 32 publications

References 24 publications

QCD3 and the replica method

QCD3 and the replica method

3D two-color QCD at finite temperature and baryon density

Random matrix model forQCD3staggered fermions

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