QCD with Large Number of Quarks: Effects of the Instanton -- Anti-instanton Pairs

We calculate the contribution of the instanton -- anti-instanton ($I\bar I$) pairs to the vacuum energy of QCD-like theories with $N_f$ light fermions using the saddle point method. We find a qualitative change of the behavior: for $N_f \ge 6$ it starts to oscillate with $N_f$. Similar behaviour was known for quantum mechanical systems interacting with fermions. We discuss the possible consequences of this phenomenon, and its relation to the mechanism of chiral symmetry breaking in these theories. We also discuss the asymptotics of the perturbative series associated with the $I\bar I$ contribution, comparing our results with those in literature.Comment: 11 pages, Late

Mean Field, Instantons and Finite Baryon Density

Instantons create a non-local interaction between the quarks, which at finite baryon density leads to the formation of a scalar diquark condensate and color superconductivity. A mean field approach leads to a self-consistent description of the $$and$$ condensates and shows the inevitability of a BCS type instability at the Fermi surface. The role of the rearrangement of the instanton ensemble for the QCD phase transitions is also discussed.Comment: 7 pages LaTeX, 3 eps-figures included, to appear in the Proc. of the 'QCD at Finite Baryon Density'-Workshop (Bielefeld, 27.-30.04.98

Observation of Topological Weyl Type I-II Transition in Synthetic Mechanical Lattices

Weyl points are three-dimensional linear points between bands that exhibit unique stability to perturbations and are accompanied by topologically non-trivial surface states. However, the discovery and control of Weyl points in nature poses significant challenges. While recent advances have allowed for engineering Weyl points in photonic crystals and metamaterials, the topological transition between Weyl semimetals with distinct types of Weyl points remains yet to be reported. Here, exploiting the flexible measurement-feedback control of synthetic mechanical systems, we experimentally simulate Weyl semimetals and observe for the first time the transition between states with type-I and type-II Weyl points. We directly observe the change in the band structures accompanying the transition and identify the Fermi arc surface states connecting the Weyl points. Further, making use of the non-reciprocal feedback control, we demonstrate that the introduction of non-Hermiticity significantly impacts the topological transition point, as well as the edge localization of the Fermi arc surface states. Our findings offer valuable insights into the design and realization of Weyl points in mechanical systems, providing a promising avenue for exploring novel topological phenomena in non-Hermitian physics

Interaction-driven breakdown of Aharonov--Bohm caging in flat-band Rydberg lattices

Flat bands play a central role in hosting emergent states of matter in many condensed matter systems, from the nascent insulating states of twisted bilayer graphene to the fractionalized excitations found in frustrated magnets and quantum Hall materials. Here, we report on the experimental realization of highly tunable flat-band models populated by strongly interacting Rydberg atoms. Using the approach of synthetic dimensions, we engineer a flat-band rhombic lattice with twisted boundaries, and through nonequilibrium dynamics we explore the control of Aharonov--Bohm (AB) caging via a tunable $U(1)$ gauge field. Through microscopic measurements of Rydberg pairs, we explore the interaction-driven breakdown of AB caging in the limit of strong dipolar interactions that mix the lattice bands. In the limit of weak interactions, where caging remains intact, we observe an effective magnetism that arises due to the interaction-driven mixing of degenerate flat-band states. These observations of strongly correlated flat-band dynamics open the door to explorations of new emergent phenomena in synthetic quantum materials.Comment: 7 pages, 4 figure

Pion and Eta Strings

In this paper we construct a string-like classical solution, the pion-string, in the linear sigma model. We then study the stability of the pion-string, and find that it is unstable in the parameter space allowed experimentally. We also speculate on the existance of an unstable eta-string, associated with spontaneous breakdown of the anomalous $U_A(1)$ symmetry in QCD at high temperatures. The implications of the pion and eta strings for cosmology and heavy ion collisions are briefly mentioned.Comment: 5 pages, LATE

Chiral phase transition at finite temperature and conformal dynamics in large Nf QCD

We investigate the chiral phase transition at finite temperature (T) in colour SU(Nc=3) Quantum Chromodynamics (QCD) with six species of fermions (Nf=6) in the fundamental representation by using lattice QCD with improved staggered fermions. By considering lattices with several temporal extensions Nt, we observe asymptotic scaling for Nt > 4. We then extract the dimensionless ratio Tc/Lambda_L (Lambda_L = Lattice Lambda-parameter) for Nf = 6 and Nf = 8, the latter relying on our earlier results. Further, we collect the critical couplings beta^c for the chiral phase transition at Nf = 0 (quenched), and Nf = 4 at a fixed Nt = 6. The results are consistent with enhanced fermionic screening at larger Nf. The Tc/Lambda_L depends very mildly on Nf in the Nf = 0 - 4 region, starts increasing at Nf = 6, and becomes significantly larger at Nf = 8, close to the edge of the conformal window. We discuss interpretations of these results as well as their possible interrelation with preconformal dynamics in the light of a functional renormalization group analysis.Comment: 8 pages, 9 figure

Diquark Bose Condensates in High Density Matter and Instantons

Instantons lead to strong correlations between up and down quarks with spin zero and anti-symmetric color wave functions. In cold and dense matter, $n_b>n_c\simeq 1 fm^{-3}$ and $T<T_c\sim$ 50 MeV, these pairs Bose-condense, replacing the usual $$condensate and restoring chiral symmetry. At high density, the ground state is a color superconductor in which diquarks play the role of Cooper pairs. An interesting toy model is provided by QCD with two colors: it has a particle-anti-particle symmetry which relates$$ and $$ condensates.Comment: 4 pages ReVTeX, 2 eps-figures included using epsf.st

Confinement- Deconfinement Phase Transition in Hot and Dense QCD at Large N

We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N and N_f\ll N at T\neq 0 and \mu\neq 0 is triggered by the drastic change in \theta behavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at the value of temperature T=T_c where \theta dependence experiences a sudden change in behavior[1]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the \theta dependence) are under complete theoretical control for T>T_c, suddenly break down immediately below T<T_c with sharp changes in the \theta dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement -deconfinement phase transition of dense QCD at large \mu in large N limit by analyzing the \theta dependence. We find that the confinement- deconfinement phase transition at N_f\ll N happens at very large quark chemical potential \mu_c\sim \sqrt{N}\Lambda_{QCD}. This result agrees with recent findings by McLerran and Pisarski[2]. We also speculate on case when N_f\sim N.Comment: 10 pages, final version to appear in Nucl. Phys.

Wilsonian Matching of Effective Field Theory with Underlying QCD

We propose a novel way of matching effective field theory with the underlying QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive Wilsonian matching conditions between current correlators obtained by the operator product expansion in QCD and those by the hidden local symmetry (HLS) model. This determines without much ambiguity the bare parameters of the HLS at the cutoff scale in terms of the QCD parameters. Physical quantities for the pi and rho system are calculated by the Wilsonian RGE's from the bare parameters in remarkable agreement with the experiment.Comment: 13 pages, 4 figures, Minor corrections. This is the version to appear in Physical Review