Instanton effects and chiral symmetry breaking in QCD2

This is a review of the QCD instanton vacuum. After introducing instantons and their physical meaning, I show that the number of instantons in the vacuum fluctuates in accordance with the QCD trace anomaly. The main properties of the instanton ensemble are given. Chiral symmetry breaking by instantons is explained in three different though mathematically equivalent ways. In particular, a derivation of the Nambu--Jona-Lasinio-type model from instantons is presented, and the ef...

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 no...

This is the second paper of the series aimed at understanding the ensemble of instanton-dyons, now with two flavors of light dynamical quarks. The partition function is appended by the fermionic factor, $(det T)^{N_f}$ and Dirac eigenvalue spectra at small values are derived from the numerical simulation of 64 and 128 dyons. Those spectra show clear chiral symmetry breaking pattern at high dyon density.

We present the results of a recent investigation of the short-distance structure of non-perturbative interaction between light quarks. We analyze the connection between topology and the dynamics responsible for the spontaneous breaking of chiral symmetry. By measuring some appropriate correlation functions on the lattice, we provide compelling evidence for instanton-induced dynamics.

We analyze the formation of fermionic condensates in two dimensional quantum chromodynamics for matter in the fundamental representation of the gauge group. We show that a topological regular instanton background is crucial in order to obtain nontrivial correlators. We discuss both massless and massive cases.

This talk is a review of our studies of instantons and their properties as seen in our lattice simulations of SU(2) gauge theory. We have measured the topological susceptibility and the size distribution of instantons in the QCD vacuum. We have also investigated the properties of quarks moving in instanton background field configurations, where the sizes and locations of the instantons are taken from simulations of the full gauge theory. By themselves, these multi-instanton...

We investigate chiral symmetry breaking and color symmetry breaking in QCD. The effective potential of the corresponding scalar condensates is discussed in the presence of non-perturbative contributions from the semiclassical one-instanton sector. We concentrate on a color singlet scalar background which can describe chiral condensation, as well as a color octet scalar background which can generate mass for the gluons. Whereas a non-vanishing singlet chiral field is favored b...

In this work we present the results from numerical simulations of an interacting ensemble of instanton-dyons in the $SU(3)$ gauge group with $N_f=2$ flavors of massless quarks. Dynamical quarks are included via the effective interactions induced by the fermionic determinant evaluated in the subspace of topological zero modes. The eigenvalue spectrum of the Dirac operator is studied at different volumes to extract the chiral condensate and eigenvalue gap, with both observables...

To elucidate the role played by instantons in chiral symmetry breaking, we explore their properties in full QCD, around the critical temperature. We study in particular spatial correlations between low-lying Dirac eigenmodes and instantons. Our measurements are compared with the predictions of instanton-based models.

We argue that instantons play a crucial role in triggering the spontaneous breaking of chiral symmetry in the physics of the three light quarks in quantum chromodynamics. However, instantons may also play an essential role in our understanding of the suppression of CP violation in the strong interactions. We revive the possibility that the bare mass of the up quark is identically zero and the apparent small up quark mass is generated by the effective quark dynamics associated...