Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and nonzero expectation value of $A_4$. While the interaction between instanton-dyons has been calculated to one-loop order by a number of authors, that for dyon-antidyon pairs remains unknown even at the classical level. In this work we are filling this gap, by solving the gradient flow equation on a 3d lattice. We start with two well separated objects. We find that, after initial rapid relaxation, the configurations follow "streamline" set of configurations, which is basically independent on the initial configurations used. In striking difference to instanton-antiinstanton streamlines, in this case it ends at a quasi-stationary configuration, with an abrupt drop to perturbative fields. We parameterize the action of the streamline configurations, which is to be used in future many-body calculations.
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.
Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and holonomy. We perform numerical simulations of the ensemble of interacting dyons for the SU(2) pure gauge theory. Unlike previous studies, we focus on back reaction on the holonomy and the issue of confinement. We calculate the free energy as a function of the holonomy and the dyon densities, using standard Metropolis Monte Carlo and integration over parameter methods. We observe that as the temperature decreases and the dyon density grows, its minimu…
It is known since 1980's that the instanton-induced 't Hooft effective Lagrangian not only can solve the so called $U(1)a$ problem, by making the $η'$ meson heavy etc, but it can also lead to chiral symmetry breaking. In 1990's it was demonstrated that, taken to higher orders, this Lagrangian correctly reproduces effective forces in a large set of hadronic channels, mesonic and baryonic ones. Recent progress in understanding gauge topology at finite temperatures is related with the so called {\em instanton-dyons}, the constituents of the instantons. Some of them, called $L$-dyons, possess the …
The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromo-magnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (non-supersymmetric) theories. Recently a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a…
We revisit the instanton-dyon liquid model in the confined phase by using a non-linear Debye-Huckel (DH) resummation for the Coulomb interactions induced by the moduli, followed by a cluster expansion. The organization is shown to rapidly converge and yields center symmetry at high density. The dependence of these results on a finite vacuum angle are also discussed. We also formulate the hypernetted chain (HCN) resummation for the dense instanton-dyon liquid and use it to estimate the liquid pair correlation functions in the DH limit. At very low temperature, the dense limit interpolates betwe…
We study the confinement phase transition in $SU(2)$ Yang-Mills theory, based on a statistical ensemble model of correlated instanton-dyons. We show for the first time that such a model provides a quantitative description, in light of the lattice data, for the temperature dependence of the order parameter. We characterize the short-range interaction which plays a crucial role for the properties of such ensemble. The chromo-magnetic charge density as well as the spatial correlations is found to be consistent with known lattice and phenomenological information.
We calculate exactly functional determinants for quantum oscillations about periodic instantons with non-trivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with non-trivial holonomy occur in the Yang--Mills partition function. The weight depends on the value of the holonomy, the temperature, Lambda_QCD, and the separation between the BPS monopoles (or dyons) which constitute the periodic instanton. At large separation between constituent dyons, the quantum measure factorizes into a product of individual dyon measures, times …
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 providing consistent values of the chiral transition temperature $T_c$. We find that a sufficient density of dyons is r…
Confinement remains one the most interesting and challenging nonperturbative phenomenon in non-Abelian gauge theories. Recent semiclassical (for SU(2)) and lattice (for QCD) studies have suggested that confinement arises from interactions of statistical ensembles of instanton-dyons with the Polyakov loop. In this work, we extend studies of semiclassical ensemble of dyons to the $SU(3)$ Yang-Mills theory. We find that such interactions do generate the expected first-order deconfinement phase transition. The properties of the ensemble, including correlations and topological susceptibility, are s…
We discuss an extension of the instanton-dyon liquid model that includes light quarks at finite chemical potential in the center symmetric phase. We develop the model in details for the case of SU_c(2)\times SU_f(2) by mapping the theory on a 3-dimensional quantum effective theory. We analyze the different phases in the mean-field approximation. We extend this analysis to the general case of SU_c(N_c)\times SU_f(N_f) and note that the chiral and diquark pairings are always comparable.
We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit $Z_{N_c}$ symmetry for the case with equal number of colors $N_c$ and flavors $N_f$. We map the model on a 3-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for $N_f=N_c=2, 3$. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with $N_f-1$ massless pions. The high temperature phase breaks center symmetry b…
We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective t…
Instantons at finite temperature consist of dyons, with their masses depending on the asymptotic Polyakov loop. It is shown that the suppression of heavy dyons can explain qualitatively the behavior of the periodic and antiperiodic chiral condensate and the topological susceptibility above the phase transition.
"Exotic quarks" in the title refers to a modification of quark periodicity condition on the thermal circle by introduction of some phases -- known also as "flavor holonomies" -- different quark flavors. These phases provide a valuable tool, to be used for better understanding of deconfinement and chiral restoration phase transitions: by changing them one can dramatically modify both phase transitions. In the language of instanton constituents -- instanton-dyons or monopoles -- it has a very direct explanation: the interplay of flavor and color holonomies can switch topological zero modes betwe…
In the instanton ensemble the fermionic zero modes collectivize and break chiral symmetry. Recent studies of resulting zero mode zone confirm its very small width and overall importance for lattice simulations. Confinement however has been related with completely different topological objects, the magnetic monopoles. Instanton constituents -- instanton dyons, discovered at nonzero holonomy by Pierre van Baal and others -- are able to explain both confinement and chiral symmetry breaking. The talk summarizes recent works deriving the instanton-dyon mutual interactions, and statistical studies o…
The functional determinant is computed exactly for quantum oscillations about periodic instantons with non-trivial values of the Polyakov line at spatial infinity (or holonomy). Such instantons can be viewed as composed of the Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. We find the weight or the probability with which dyons occur in the pure Yang--Mills partition function. It turns out that dyons experience quantum interactions having the familiar "linear plus Coulomb" form but with the "string tension'' depending on the holonomy. We present an argument that at temperatures below …
Paradigme shift in gauge topology, from instantons to their constituents -- instanton-dyons -- has recently lead to very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at sufficiently high density explains the chiral symmetry breaking. Unlike instantons, these objects have electric and magnetic charges. Their back reaction on the mean value of the Polyakov line (holonomy) allows to explain the deconfinement transition. The talk summarizes recent works on the dyon ensemble, done in the mean field approximation (MFA), and also by direct numerica…
We start with the relation between the chiral symmetry breaking and gauge field topology. New lattice result further enhance the notion of Zero Mode Zone, a very narrow strip of states with quasizero Dirac eigenvalues. Then we move to the issue of "origin of mass" and Brown-RHo scaling: a number of empirical facts contradicts to the idea that masses of quarks and such hadrons as $ρ,N$ decrease near $T_c$. We argue that while at $T=0$ the main contribution to the effective quark mass is chirally odd $m_{\snchi}$, near $T_c$ it rotates to chirally-even component $m_χ$, because "infinite clusters…
These are lecture notes, which summarize the current status of the Semiclassical theory, as well as Monopoles, Instantons, Instanton-dyons and Flux tubes. The emphasis is on QCD and QCD-like theories (deformed QCD), although relevant points derived in Supersymmetric theories are also covered. While the actual lectures on which the notes are based were delivered in the fall 2018, the text evolved over the years and summarizes about 4 decades of development. One recent point added is the so called Poisson duality between monopoles and instanton-dyon approaches. It is made in a book format, with …
We study the vacuum topology of 2+1 flavor QCD above the chiral crossover transition, at $T \lesssim 1.2~T_c$, on lattices of size $32^3\times 8$. Since overlap fermions have exact chiral symmetry and an index theorem even on a finite lattice, we use them to detect the topological content of gauge fields generated using domain wall fermion discretization for quarks. We further use different periodicity phases along the temporal direction for the valence overlap quarks, which allows us to probe different topological structures present in the gauge field ensembles, through its zero modes. This p…
Instanton-dyons are topological solitons -- solutions of Yang-Mills equations -- which appear at non-trivial expectation value of $A_0$ at nonzero temperatures. Using the ensembles of those, generated in our previous work, for 2-color and 2-flavor QCD, below and above the deconfinement-chiral phase transition, we study the correlations between them, as well as fluctuations of several global charges in the sub-volumes of the total volume. The determined correlation lengths are the finite-$T$ extension of hadronic masses, such as that of $η'$ meson.
