Related papers: Poincar\'e recurrence theorem and the strong CP-pr…
An exact duality between axion with arbitrary potential and antisymmetric form-field has been derived some time ago. Using this duality, the axion solution to strong-CP problem has been formulated as a gauge invariant theory of forms. In…
Peccei-Quinn (PQ) mechanism based on a chiral global U(1) symmetry is considered to be a simple and elegant solution for strong CP problem. Fact that the mechanism could be experimentally examined through the axion search makes it much more…
Assuming that a non-trivial quantum Yang-Mills theory exists, we have proved that it should have a mass gap $\Delta^2 > 0$, indeed. The proof is based on the derivation of the novel constraint on any solution to QCD. It has been exactly and…
QCD and related gauge theories have a sign problem when a $\theta$-term is included; this complicates the extraction of physical information from Euclidean space calculations as one would do in lattice studies. The sign problem arises in…
In the effective field theory framework, we consider the effect of supersymmetry breaking via gaugino condensation and supergravity in the hidden sector gauge group on the hidden sector vacuum angle $\theta_h$. The $\theta_h$ parameter…
In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C), spatial reflection (P) and time reversal (T) are spontaneously broken in QCD. The order parameter for the symmetry…
These lecture notes provide a self-contained, graduate-level introduction to the strong $CP$ problem and QCD axion physics from an effective field theory (EFT) viewpoint. We review the construction of the chiral EFT of QCD yielding a…
Using the effective potential approach for composite operators we have formulated the quantum model of the QCD vacuum. It is based on the existence and importance of the nonperturbative $q^{-4}$-type dynamical, topologically nontrivial…
An analytic ghost-free model for the QCD running coupling $\alpha(Q^2)$ is proposed. It is constructed from a more general approach we developed particularly for investigating physical observables of the type $F(Q^2)$ in regions that are…
We study gauge theories in the context of a gravitational theory without the cosmological constant problem (CCP). The theory is based on the requirement that the measure of integration in the action is not necessarily $\sqrt{-g}$ but it is…
We begin with the discussion of the relationship between the trace of the energy momentum tensor and the gluon condensate at finite temperatures. Using the recent numerical data from the simulations of lattice gauge theory for quantum…
In these proceedings, I shall review the basic concepts of perturbative QCD in its high-energy limit. I shall concentrate on the approach to the unitarity limit, usually referred to as saturation, as well as on the gluon-number fluctuations…
The QCD axion stands as one of the most promising candidates for resolving the strong CP problem. However, the value of the axion's decay constant $f_a$ and, by extension, its mass $m_a$, remain uncertain within the framework of effective…
While $CP$ violation has never been observed in the strong interactions, the QCD Lagrangian admits a $CP$-odd topological interaction proportional to the so called $\theta$ angle, which weighs the contributions to the partition function…
Nucleus-nucleus interaction is studied in the framework of the perturbative QCD with large number of colours and a fixed coupling constant. The pomeron tree diagrams are summed by an effective field theory. The classical field equations are…
An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is briefly reviewed. These fields play the role of the confining medium for color…
There is considerable freedom in setting boundary conditions to perturbation theory at $t=\pm\infty$. The standard PQED and PQCD expansions are based on the (empty) perturbative vacuum. Since the true QCD ground state is expected to have a…
QCD in 0+1 dimensions is numerically solved via thimble regularization. In the context of this toy model, a general formalism is presented for SU(N) theories. The sign problem that the theory displays is a genuine one, stemming from a…
We study the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant $I_2=\vec{E}\cdot{\vec B}$. We show that the presence of $I_2$ can induce neutral pion ($\pi^0$) condensation in the…
We propose a new topological charge term in QCD based on flux-tube models. It couples a superflow of the phase of the quark condensate to the Chern-Simons current. The usual $\theta$-parameter is replaced by the phase of the quark…