Narrow Results

QCD instantons generate non-perturbative spin- and flavor- dependent correlations between light quarks. We report on the results of a series of studies on the contribution of instantons to the electro-weak structure of light hadrons. We show that the Instanton Liquid Model can reproduce the available data on proton and pion form factors at large momentum transfer, and explain the delay of the onset of the perturbative regime in some exclusive reactions. We provide unambiguous evidence that instantons lead to the formation of a deeply bound scalar, color anti-triplet diquark, with a mass of about 450 MeV. The strong attraction in the , scalar diquark channel leads to a quantitative description of non-leptonic decays of hyperons and provides a microscopic dynamical explanation of the Δ I = 1/2 rule.

We review basic aspects of worldsheet and penta-brane instantons as well as (unoriented) D-brane instantons, which is our main focus here, and threshold corrections to BPS-saturated couplings. We then consider nonperturbative superpotentials generated by "gauge" and "exotic" instantons living on D3-branes at orientifold singularities. Moreover, we discuss the interplay between worldsheet and D-string instantons on T⁴/Z₂. We focus on a 4-Fermi amplitude, give Heterotic and perturbative Type I descriptions, and offer a multi-D-string instanton interpretation. We conclude with possible interesting developments.

We conjecture that the confinement–deconfinement phase transition in QCD at large number of colors N and N_f ≪ N at T ≠ 0 and µ ≠ 0 is triggered by the drastic change in θ behavior. The conjecture is motivated by the holographic model of QCD where confinement–deconfinement phase transition indeed happens precisely at T = T_c where θ dependence experiences a sudden change in behavior. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the θ dependence) are under complete theoretical control for T > T_c, suddenly break down immediately below T < T_c with sharp changes in the θ dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement–deconfinement phase transition of hot and dense QCD in large N limit by analyzing the θ dependence. We estimate the critical values for T_c and µ_c where the phase transition happens by approaching the critical values from the hot and/or dense regions where the instanton calculations are under complete theoretical control. We also describe some defects of various codimensions within a holographic model of QCD by focusing on their role around the phase transition point.

Monopoles and instantons are sheets (membranes) and strings in d = 5+1 dimension, respectively, and instanton strings can terminate on monopole sheets. We consider a pair of monopole and antimonopole sheets which is unstable to decay and results in a creation of closed instanton strings. We show that when an instanton string is stretched between the monopole sheets, there remains a new topological soliton of codimension five after the pair annihilation, i.e. a twisted closed instanton string or a knotted instanton.

In this paper, we study a class of grand-canonical partition functions with a kernel depending on a small parameter ϵ. This class is directly relevant to Nekrasov partition functions of 𝒩 = 2 SUSY gauge theories on the 4d Ω-background, for which ϵ is identified with one of the equivariant deformation parameter. In the Nekrasov–Shatashvili limit ϵ→0, we show that the free energy is given by an on-shell effective action. The equations of motion take the form of a TBA equation. The free energy is identified with the Yang–Yang functional of the corresponding system of Bethe roots. We further study the associated canonical model that takes the form of a generalized matrix model. Confinement of the eigenvalues by the short-range potential is observed. In the limit where this confining potential becomes weak, the collective field theory formulation is recovered. Finally, we discuss the connection with the alternative expression of instanton partition functions as sums over Young tableaux.

Because of the presence of a cosmological horizon, the dilute instanton gas approximation used for the derivation of the Coleman–De Luccia tunneling rate in de Sitter space–time receives additional contributions due to the finite instanton separation. Here, I calculate the first corrections to the vacuum decay rate that arise from this effect and depend on the parameters of the theory and the cosmological constant of the background space–time.

Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when $E\approx m$ (or infrared limit). In this infrared approximation the theory ${\phi }^4$ is formally two-dimensional and its Euclidean solutions are instantons. For BPST-like solutions with $A_{\mu }^a=A_{\mu }^a(x^2)$, the map between ${\phi }^4$ in two dimensions and self-dual Yang–Mills theory is carefully discussed.

In this paper, an infinite-dimensional Laplacian defined as the Cesáro mean of the second-order directional derivatives on manifold is considered. This Laplacian is parametrized by the choice of a curve in the group of orthogonal rotations. It is shown that under certain conditions on the curve, this operator is related to instantons on a four-dimensional manifold.

We examine a generalization of the usual self-duality equations for Yang–Mills theory when the color space admits a nontrivial involution. This involution allows us to construct a nontrivial twist which may be combined with the Hodge star to form a twisted self-dual curvature. We will construct a simple example of twisted self-duality for $su(2)\oplus su(2)$ gauge theory along with its explicit solutions, both in Euclidean and Minkowski backgrounds, and then dimensionally reduce from four dimensions to obtain families of nontrivial nonlinear equations in lower dimensions. This twisted self-duality constraint will be shown to arise in $E_7$ exceptional field theory through a Scherk–Schwarz reduction and we will show how an Eguchi–Hanson gravitational instanton also obeys the twisted self-duality condition.

A new exact time-dependent Kerr-like black hole solution is found on a Randall–Sundrum brane world spacetime. The solution is also valid on the Wick-rotated Euclidean counterpart space, so represents equally well a gravitational instanton, i.e. a bump in spacetime. Since the r-dependent part is determined by a first-order differential equation, one conjectures that the solution is a self-dual solution comparable with the Eguchi–Hanson solution. The zeroes and poles of the spacetime are determined by a quintic polynomial. To describe the Hawking particles, one uses the antipodal boundary condition on a complex Klein-bottle hypersurface ${ℂ}^1\times {ℂ}^1$. We used the Hopf fibration to get $S^2$ as the black hole horizon, where the centrix is not in a torus but in the Klein bottle. The twist fits very well with the antipodal identification of the point on the horizon. No “cut-and-paste” is necessary, so the Hawing particles remain pure without instantaneous information transport. A local observer passing the horizon will not notice a central singularity in suitable coordinates. The black hole paradoxes are also revisited in our new black hole model. A connection is made with the geometric quantization of ${ℂ}^1\times {ℂ}^1\sim S^3$, by considering the symplectic 2-form. The model can be easily extended to the non-vacuum situation by including a scalar field. Both the dilaton and the scalar field can be treated as quantum fields when approaching the Planck area.

Quantum phase slips can induce a phase transition in a single Josephson junction by varying coupling strength R_S to the dissipative environment. We study the finite Josephson junction array with dissipations. For the infinite arrays with no dissipation, a quantum KT phase transition can occur by varying the ratio of the Josephson coupling strength E_J to the charging energy E_c due to the unbinding of instanton pairs. At finite temperature and array size, there will be a rich interplay between instantons and quantum phase slips.

Quantum tunneling of vortices had been found to be an important novel phenomena for description of low temperature creep in high temperature superconductors (HTSCs). We speculate that quantum tunneling may be also exhibited in mesoscopic superconductors due to vortices trapped by the Bean-Livingston barrier. The London approximation and method of images is used to estimate the shape of the potential well in superconducting HTSC quantum dot. To calculate the escape rate we use the instanton technique. We model the vortex by a quantum particle tunneling from a two-dimensional ground state under magnetic field applied in the transverse direction. The resulting decay rates obtained by the instanton approach and conventional WKB are compared revealing complete coincidence with each other.

In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-Abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang–Mills instantons, whose solutions can be constructed from the celebrated Atiyah–Drinfeld–Hitchin–Manin (ADHM) construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a regime are necessarily in a solid crystalline phase. In this review, we summarize the known results on the construction and phases of crystals of the holographic baryons.

We present exact Coleman–De Luccia (CDL) instantons, which describe vacuum decay from Anti-de Sitter (AdS) space, de Sitter (dS) space and Minkowski space to AdS space. We systematically obtain these exact solutions by considering deformation of Hawking-Moss (HM) instantons. We analytically calculate the action of instantons and discuss a subtlety in calculation of decay rates.

Unlike flat space quantum field theories that focus on scattering amplitudes, the main observables in quantum cosmology are correlation functions. The systematic way of calculating correlators is called in–in formalism, which requires only a single asymptotic region, i.e. past infinity. The rules in perturbation theory and the path integral measure are very different for in–in and in–out formalisms, and thus the results which are standard in one approach may not necessarily hold in the other one. We show that stationary phase approximation works completely different for a scalar in–in path integral. Hence, in a cosmological background there are solutions, pseudo-instantons, that allow tunneling between locally stable vacua even in infinite volume, which is counterintuitive from an in–out perspective. We argue that various familiar notions of in–out formalism must be re-examined in the in–in formalism, which might have important consequences for quantum cosmology.

Paradigm shift in gauge topology, from instantons to their constituents — instanton-dyons — has recently lead to very significant advances. Unlike instantons, these objects have three different set of charges, therefore allowing to explain and to tie together several important phenomena: confinement, chiral symmetry breaking and magnetic screening.

The equivalence of the anti-selfduality Yang–Mills equations on the four-dimensional orientable Riemannian manifold and the Laplace equations for some infinite-dimensional Laplacians is proved. A class of modified Lévy Laplacians parameterized by the choice of a curve in the group $\mathrm{\text{SO}}(4)$ is introduced. It is shown that a connection is an instanton (a solution of the anti-selfduality Yang–Mills equations) if and only if the parallel transport generalized by this connection is a solution of the Laplace equations for some three modified Lévy Laplacians from this class.

Building on a variation of 't Hooft's harmonic function ansatz for SU(2) instantons on ℝ⁴, we provide new explicit nonsingular solutions of the Yang–Mills anti-self-duality equations on Euclidean spacetime with gauge group SL(2, ℂ) and SL(3, ℝ).

It is shown that if the contribution of flat connections on the dimension of the moduli spaces of Yang–Mills instantons and anti-instantons is appropriately taken into the account, then the inadmissible cases of negative dimensions may be reduced to zero-dimensional moduli spaces, corresponding to a collection of points, and whose counting will correspond to the Donaldson invariant of the base manifold. These results will lead to a possible description of that invariant in terms of flat connections with diverse applications, for example for testing the conjecture on its equivalence to the Seiberg–Witten invariant, and for the study of the qualitative and quantitative aspects of the gauge/gravity duality.

In this note we study a correspondence between the space of three-forms on a four-manifold and the space of three-forms on the moduli space of instantons. We then specialize to the case where the base manifold is the four-sphere.