Light quark masses and condensates in QCD

This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete 't Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-q N -flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete 't Hooft anomaly matching to theories on R 2 and its compactification to R × S 1 L . We then compare the 't Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are N q vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e iθ/N q , which provides the N q-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by "quantum" instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-N limit of the Schwinger model with twisted boundary conditions satisfy volume independence. arXiv:1905.05781v3 [hep-th]

Section: Discrete 'T Hooft Anomaly and Four-fermion Interactionmentioning

confidence: 99%

Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Misumi

Tanizaki

Ünsal

2019

“…In this section, we examine an exotic scenario of the chiral-symmetry broken phase of QCD, proposed by Stern [61,62] based on symmetries and anomalies. In a previous study [63], this phase has been ruled out based on QCD inequalities, so it cannot be realized as the QCD vacuum at the zero baryon density.…”

Section: Ruling Out Chiral Symmetry Breaking Without Quark Bilinear Cmentioning

confidence: 99%

“…The conventional order parameter of chiral symmetry breaking is the chiral condensate ψψ = ψ R ψ L + ψ L ψ R , and the pion decay constant f π is another important parameter. Stern pointed out that the condition f π = 0 does not necessarily require that ψψ = 0, and suggested the exotic chiral-symmetry broken phase with f π = 0 and ψψ = 0 [61]. The local order parameter for this phase is the four-quark condensate [63], such as…”

Section: Ruling Out Chiral Symmetry Breaking Without Quark Bilinear Cmentioning

confidence: 99%

Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking

Tanizaki¹

2018

We discuss consequences of the 't Hooft anomaly matching condition for Quantum Chromodynamics (QCD) with massless fundamental quarks. We derive the new discrete 't Hooft anomaly of massless QCD for generic numbers of color N c and flavor N f , and an exotic chiral-symmetry broken phase without quark-bilinear condensate is ruled out from possible QCD vacua. We show that the U (1) B baryon number symmetry is anomalously broken when the (Z 2N f ) A discrete axial symmetry and the flavor symmetry are gauged. In the ordinary chiral symmetry breaking, the Skyrmion current turns out to reproduce this 't Hooft anomaly of massless QCD. In the exotic chiral symmetry breaking, however, the anomalous breaking of U (1) B does not take the correct form, and it is inconsistent with anomaly matching. This no-go theorem is based only on symmetries and anomalies, and thus has a wider range of applicability to the QCD phase diagram than the previous one obtained by QCD inequalities. Lastly, as another application, we check that duality of N = 1 supersymmetric QCD with N f ≥ N c + 1 satisfies the new anomaly matching.

“…While spontaneous symmetry breaking in all these cases can be characterized by a nonvanishing fermion bilinear condensate, symmetry breaking in general can also be triggered by higher-order condensates. In QCD it was stressed by Stern that chiral symmetry breaking with F π = 0 does not necessitate ψψ = 0 [38,39]. Indeed one can imagine a situation where chiral condensate is forbidden by an anomaly-free discrete subgroup of U(1) A and the spontaneous breaking SU(N f ) R × SU(N f ) L → SU(N f ) V is driven by a quartic condensate.…”

Section: Introductionmentioning

confidence: 99%

Heavy-tailed chiral random matrix theory

Kanazawa¹

2016

We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.Comment: 18 pages, 5 figure