Instantons and color symmetry breaking in the vacuum (original) (raw)
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Instantons and spontaneous color symmetry breaking
Physics Letters B, 2002
The instanton interaction in QCD generates an effective potential for scalar quark-antiquark condensates in the color singlet and octet channels. For three light quark flavors the cubic term in this potential induces an octet condensate and "spontaneous breaking" of color in the vacuum. Realistic masses of the ρ-and η ′ -mesons are compatible with renormalization-group-improved instanton perturbation theory. * We take the opportunity to correct the instanton vertex of . It was based on the Fierz transform of an uncorrect vertex quoted in .
Possible color octet quark-antiquark condensate in the instanton model
Physical Review D, 2001
Inspired by a recent proposal for a Higgs description of QCD we study the possible formation of a color-octet/flavor-octet quark-anti-quark condensate in the instanton liquid model. For this purpose we calculate two-point correlation functions of color-singlet and octet quark-anti-quark operators. We find long range order in the standard ψ ψ channel, but not in the color-octet channel. We emphasize that similar calculations in lattice QCD can check whether or not a color-flavor locked Higgs phase is realized in QCD at zero temperature and baryon density.
High-Density QCD and Instantons
Annals of Physics, 2000
Instantons generate strong non-perturbative interactions between quarks. In the vacuum, these interactions lead to chiral symmetry breaking and generate constituent quark masses on the order of 300-400 MeV. The observation that the same forces also provide attraction in the scalar diquark channel leads to the prediction that cold quark matter is a color superconductor, with gaps as large as ∼ 100 MeV. We provide a systematic treatment of color superconductivity in the instanton model. We show that the structure of the superconductor depends on the number of flavors. In the case of two flavors, we verify the standard scenario and provide an improved calculation of the mass gap. For three flavors, we show that the ground state is color-flavor locked and calculate the chiral condensate in the high density phase. We show that as a function of the strange quark mass, there is a sharp transition between the two phases. Finally, we go beyond the mean-field approximation and investigate the role of instanton-antiinstanton molecules, which-besides superconducting gap formation-provide a competitive mechanism for chiral restoration at finite density.
A Mechanism for Instanton Induced Chiral Symmetry Breaking in QCD
Arxiv preprint hep-ph/9507297, 1995
We propose a mechanism for instanton induced chiral symmetry breaking in QCD with fundamental scalars. The model Lagragian that we use has the same symmetry properties as QCD. The scalar fields develop vacuum expectation values at a non-trivial minimum and generate masses for thhe light quarks. The minimization condition is also used to break the SU (N f ) flavour symmetry in order to make the s quark heavier than the two lighter ones. Thus a vacuum of the theory that is not chirally invariant is obtained.
Instanton induced chiral symmetry breaking in extended QCD model
The European Physical Journal C, 1998
A mechanism for instanton induced chiral symmetry breaking in an extended QCD model (QCD with fundamental scalars) is proposed to describe quarks and gluons inside a baryon. The model Lagrangian that we use has the same symmetry properties as QCD. The scalar fields are shown to develop vacuum expectation values in the instanton background and generate masses for the three generation of quarks. The minimization condition is also used to break the flavour symmetry to make the s-quark heavier that the u and d quarks.
Instanton condensation in field strength formulated QCD
Field strength formulated Yang-Mills theory is confronted with the traditional formulation in terms of gauge fields. It is shown that both formulations yield the same semiclassics, in particular the same instanton physics. However, at the tree level the field strength approach is superior because it already includes a good deal of of quantum fluctuations of the standard formulation. These quantum fluctuations break the scale invariance of classical QCD and give rise to an instanton interaction and this causes the instantons to condense and form a homogeneous instanton solid. Such the instanton solids show up in the field strength approach as homogeneous (constant up to gauge transformations) vacuum solutions. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color structure and carry winding number n = N (N 2 −1)/6. These instantons generate (after condensation) the lowest action solutions of the field strength approach. The statistical weight (entropy) of different homogeneous solutions for SU(3) is numerically estimated by Parisi's stochastic quantization method. Finally, we compare instanton induced quark condensation with the condensation of quarks in the homogeneous field strength solutions. Our investigations show that the homogeneous vacuum of the field strength approach simulates in an efficient way a condensate of instantons.
Reviews of Modern Physics, 1998
We review the theory and phenomenology of instantons in QCD. After a general overview, we provide a pedagogical introduction to semi-classical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. We also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. We give an overview over the role of instantons in some other models, in particular low dimensional sigma models, electroweak theory and supersymmetric QCD. 1. The gap equation for N f =1 2. The effective interaction for two or more flavors G. Bosonization and the spectrum of pseudo-scalar mesons H. Spin dependent interactions induced by instantons V. The interacting instanton liquid A. Numerical simulations B. The free energy of the instanton ensemble C. The instanton ensemble D. Dirac Spectra E. Screening of the topological charge VI. Hadronic correlation functions A. Definitions and Generalities B. The quark propagator in the instanton liquid 1. The propagator in the field of a single instanton 2. The propagator in the instanton ensemble 4. Direct instanton contributions to deep inelastic scattering and other hard processes in QCD, see (Balitskii & Braun 1993, Balitskii & Braun 1995) and the review (Ringwald & Schrempp 1994). 5. Instanton inspired models of hadrons, or phenomenological lagrangians supplemented by the 't Hooft interaction.
The QCD Vacuum as an Instanton Liquid
Annual Review of Nuclear and Particle Science, 1997
We review recent progress in understanding the importance of instanton effects in QCD. Instantons provide a mechanism for quark and gluon condensation, explain the U(1) A anomaly and the appearance of a non-perturbative vacuum energy density. In the framework of the instanton liquid model, a large number of hadronic correlation functions were calculated. The results are in good agreement with both experimental data and lattice simulations. We also review recent results on the phase structure of QCD-like theories. Instantons provide a mechanism for chiral symmetry restoration at finite temperature (or for a large number of quark flavors) connected with the formation of instanton-anti-instanton molecules.