Nonperturbative contribution to the quark form factor within the instanton model

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism, within the framework of the instanton liquid model. For the integration path corresponding to this form factor, the explicit expression for the vacuum expectation value of the Wilson operator is found to the leading order. It is shown that the instantons produce the power-like corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.-t Quantum chromodynamics - 11.15.Tk Other nonperturbative techniques     

Effect of hadronization on the form of correlation moments for instanton processes and possibility of discovering them experimentally

The possibility of discovering QCD instantons in deep-inelastic scattering by analyzing correlations in final states is studied. The correlation moments F _q and H _q for instanton processes are calculated at the parton and at the hadron level. Hadronization is taken into account by the Monte Carlo method. The moments for instanton and for usual processes are found to behave differently, which can be used to identify experimentally instantons.     

Exponential suppression of string interactions on orbifolds

Nonperturbative world-sheet instanton effects can be seen in the classical bosonic contribution to scattering amplitudes on orbifolds. These instanton contributions have the form exp(−cR²/α′) and are exponentially suppressed when the orbifold radius is large. Amplitudes whose leading contribution comes from instantons are identified with processes in which the corresponding string states are pinned to the orbifold fixed points, and unpinned amplitudes are shown to lack this suppression at large radius. Blowing up the fixed points of an orbifold eliminates any pinning and with it the corresponding exponential suppression.     

A new AF gravitational instanton

It has long been conjectured that the Euclidean Schwarzschild and Euclidean Kerr instantons are the only non-trivial asymptotically flat (AF) gravitational instantons. In this Letter, we show that this conjecture is false by explicitly constructing a new two-parameter AF gravitational instanton with a U(1)×U(1) isometry group, using the inverse-scattering method. It has Euler number χ=3 and Hirzebruch signature τ=1, and its global topology is CP² with a circle S¹ removed appropriately. Various other properties of this gravitational instanton are also discussed.     

Nonperturbative effects on factorization in high-momentum processes

It is pointed out that the usual demonstrations within QCD perturbation theory of factorization at high-momentum transfers are incomplete when nonperturbative instanton effects are incorporated in a dilute gas approximation. The apparent violation of factorization does not vanish at large Q².     

Instantons in the nonperturbative QCD vacuum

The effect of nonperturbative fields on instantons in QCD is investigated. The nonperturbative vacuum is described in terms of nonlocal gauge-invariant vacuum expectation values of gluon fields. An effective action for instantons is obtained in the bilocal approximation, and it is shown that a stochastic background gluon field leads to an infrared stabilization of instantons. The dependence of a characteristic instanton size on the magnitude of the gluon condensate and on the correlation length in the nonperturbative vacuum is found. The size distribution of instantons that is obtained here is compared with the results of lattice calculations.     

On the statistical mechanics of dense instanton gases

Instanton gases of two-dimensional?P ^n?1 and four-dimensionalSU(n) Yang-Mills theories are considered. The presumable denseness of instanton gases in these models and the corresponding statistics of instantons lead to a theormodynamic limit in which the coupling constant dependence of non-perturbative quantities is modified by a factor proportional to 1/n compared to the case of a dilute gas. As a consequence the largen limit and the infinite volume limit do not appear to commute. We present a naive droplet model for dense instanton gases which exhibits these features. Possible consequences for the large order behaviour of perturbation series are discussed.     

QCD vacuum as a disordered medium: a simplified model for the QCD dirac operator

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the dimensionless Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.     

Spin dependence of deep inelastic diffraction

Using a perturbative model for diffractive interactions, we derive an expression for the polarized diffractive structure function in the high energy limit. This structure function is given by the interference of diffractive amplitudes with polarized and unpolarized exchanges. For the polarized exchange we consider both two-gluon and quark-antiquark amplitudes. The polarized diffractive amplitude receives sizable contributions from non-strongly ordered regions in phase space, resulting in a double logarithmic enhancement at small x. The resummation of these double logarithmic terms is outlined. We also discuss the transition from our perturbative expression to the nonperturbative region. A first numerical estimate indicates that the perturbative contribution to the spin asymmetry is substantially larger than the nonperturbative one. Received: 7 July 1999 / Published online: 14 October 1999     

θ renormalization, electron-electron interactions and super universality in the quantum Hall regime

The renormalization theory of the quantum Hall effect relies primarily on the non-perturbative concept of θ renormalization by instantons. Within the generalized non-linear σ model approach initiated by Finkelstein we obtain the physical observables of the interacting electron gas, formulate the general (topological) principles by which the Hall conductance is robustly quantized and derive—for the first time—explicit expressions for the non-perturbative (instanton) contributions to the renormalization group β and γ functions. Our results are in complete agreement with the recently proposed idea of super universality which says that the fundamental aspects of the quantum Hall effect are all generic features the instanton vacuum concept in asymptotically free field theory.     

Multi-instantons and exact results II: specific cases, higher-order effects, and numerical calculations

In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton contributions to the partition function, using the formalism introduced in the first part of the treatise [Ann. Phys. (N. Y.) (previous issue) (2004)]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker-Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is non-zero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited.     

Instanton screening in the nonperturbative QCD

The gluon field screening in the stochastic vacuum of gluodynamics is studied. The effective action is derived for the instanton interacting with nonperturbative fields. Quantum nonperturbative effects are shown to affect greatly the shape of instanton. The power asymptotics x ⁻² of the classical “instanton’s profile function” at large distances is replaced due to these effects by Airy function asymptotics.     

Large Nc in nonperturbative QCD

We comment on large N_c within the context of nonperturbative QCD. In particular, we consider the QCD-based bag model, the instanton gas approximation, and the η′ mass.     

Instanton vacuum in thermal QCD

The effects of instanton-anti-instanton interactions in high-temperature QCD with colour SU(2) are studied with and without quarks. The instanton potential proves to have no repulsive core, thus creating troubles with the definition of nonperturbative contributions to physical quantities. Also the chiral condensate is calculated, and it is shown to vanish if number of quark flavoursN _f≧2, whereas forN _f=1 it is nonzero for the arbitrary high temperature.     

A new mechanism for single-spin asymmetries in strong interactions

It is shown that the contribution of instantons to the fragmentation of quarks leads to the appearance of an imaginary part in diagrams of quark-quark scattering at large transferred momentum. The imaginary part comes from the analytical continuation of the instanton amplitudes from Euclidean to Minkowsky space-time and reflects the quasiclassical origin of the instanton solution of QCD equations of motion. This phenomenon and instanton-induced quark spin-flip give a new nonperturbative mechanism for the observed anomalous single-spin asymmetries in hadron-hadron and lepton-hadron interactions.     

Higher order corrections to the Lipatov asymptotics in the ϕ<Superscript>4</Superscript> theory

Higher orders in perturbation theory can be calculated by the Lipatov method [1]. For most field theories, the Lipatov asymptotics has the functional form ca ^N Γ(N+b (N is the perturbation theory order); relative corrections to this asymptotics have the form of a power series in 1/N. The coefficients of higher order terms of this series can be calculated using a procedure analogous to the Lipatov approach and are determined by the second instanton in the field theory in question. These coefficients are calculated quantitatively for the n-component ?⁴ theory under the assumption that the second instanton is (i) a combination of elementary instantons and (ii) a spherically asymmetric localized function. A technique of two-instanton computations, as well as the method for integrating over rotations of an asymmetric instanton in the coordinate state, is developed.     

Role of anomalous chromomagnetic interaction in Pomeron and Odderon structures and in gluon distribution

We calculate the contribution arising from nonperturbative quark-gluon chromomagnetic interaction to the high-energy total quark-quark cross section and to gluon distributions in nucleon. The estimation obtained within the instanton model of QCD vacuum leads to the conclusion that this type of interaction gives the dominating contribution to the Pomeron coupling with the light quarks and to gluon distribution in light hadrons at small virtualities of quarks and gluons. We argue that the Odderon, which is the P = C = −1 partner of the Pomeron, is governed by the spin-flip component related to nonperturbative three-gluon exchange induced by anomalous quark-gluon chromomagnetic interaction.     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.     

D3 instantons in Calabi–Yau orientifolds with(out) fluxes

We investigate the instanton effects due to D3 branes wrapping a four-cycle in a Calabi–Yau orientifold with D7 branes. We study the condition for the nonzero superpotentials from the D3 instantons. To this aim we work out the zero mode structures of D3 branes wrapping a four-cycle both in the presence of the fluxes and in the absence of the fluxes. In the presence of the fluxes, the condition for the nonzero superpotential could be different from that without the fluxes. We explicitly work out a simple example of the orientifold of K3×T ²/Z ₂ with a suitable flux to show such behavior. The effects of the D3–D7 sectors are interesting and give further constraints for the nonzero superpotential. In a special configuration where D3 branes and D7 branes wrap the same four-cycle, multi-instanton calculus of D3 branes could be reduced to that of a suitable field theory. The structure of D5 instantons in Type I theory is briefly discussed.     

SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond–Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.