Non-perturbative Sector Research Articles

NONPERTURBATIVE DISPERSIVE SECTOR IN STRONG (QUASI-)ABELIAN FIELDS

In strong (quasi-)Abelian fields, even at the one-loop level of the coupling constant, quantum fluctuations of fermions induce an effective Lagrangian density whose imaginary (absorptive) part is purely nonperturbative and known to be responsible for the fermion–antifermion pair creation. On the other hand, the induced real (dispersive) part has perturbative and nonperturbative contributions. In the one-loop case, we argue how to separate the two contributions from each other for any strength of the field. We show numerically that the nonperturbative contributions are in general comparable with or larger than the induced perturbative ones. We arrive at qualitatively similar conclusions also for the induced energy density. Further, we investigate numerically the quasianalytic continuation of the perturbative results into the nonperturbative sector, by employing (modified) Borel–Padé. It turns out that in the case at hand, we have to integrate over renormalon singularities, but there is no renormalon ambiguity involved.

Nonperturbative dispersive sector in strong (quasi-)Abelian fields

In strong (quasi-)Abelian fields, even at the one-loop level of the coupling constant, quantum fluctuations of fermions induce an effective Lagrangian density whose imaginary (absorptive) part is purely nonperturbative and known to be responsible for the fermion-antifermion pair creation. On the other hand, the induced real (dispersive) part has perturbative and nonperturbative contributions. In the one-loop case, we argue how to separate the two contributions from each other for any strength of the field. We show numerically that the nonperturbative contributions are in general comparable with or larger than the induced perturbative ones. We arrive at qualitatively similar conclusions also for the induced energy density. Further, we investigate numerically the quasianalytic continuation of the perturbative results into the nonperturbative sector, by employing (modified) Borel-Pade. It turns out that in the case at hand, we have to integrate over renormalon singularities, but there is no renormalon ambiguity involved.

THE PARISI–SOURLAS MECHANISM IN YANG–MILLS THEORY?

The Parisi–Sourlas mechanism is exhibited in pure Yang–Mills theory. Using the new scalar degrees of freedom derived from the nonlinear gauge condition, we show that the nonperturbative sector of Yang–Mills theory is equivalent to a 4D O(1, 3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where [Formula: see text] is unchanged. This leads to dimensional reduction proving the equivalence of the nonperturbative sector of Yang–Mills theory to a 2D O(1, 3) sigma model.

Non-commutative unification in the brane world

We point out that in (open) string compactifications with non-zero NS–NS B-field we can have large Kaluza–Klein thresholds even in the small volume limit. In this limit the corresponding gauge theory description is in terms of a compactification on a non-commutative space (e.g., a torus or an orbifold thereof). Based on this observation we discuss a brane world scenario of non-commutative unification via Kaluza–Klein thresholds. In this scenario, the unification scale can be lowered down to the TeV-range, yet the corresponding compactification radii are smaller than the string length. We discuss a potential application of this scenario in the context of obtaining mixing between different chiral generations which is not exponentially suppressed – as we point out, such mixing is expected to be exponentially suppressed in certain setups with large volume compactifications. We also point out that T-duality is broken by certain non-perturbative twisted open string sectors which are supposed to give rise to chiral generations, so that in the case of a small volume compactification with a rational B-field we cannot T-dualize to a large volume description. In this sense, the corresponding field theoretic picture of unification via Kaluza–Klein thresholds in this setup is best described in the non-commutative language.

Light-quark meson spectroscopy with crystal barrel

Light-quark meson spectroscopy provides a powerful tool to study QCD in the non-perturbative sector. Crystal Barrel has developed a lively experimental activity over the last decade and different high-statistics results have been published which have led to stimulating theoretical interpretations. A selection of results concerning the quest of constituent gluons in hadrons will be discussed.

The dual sector of the λφ 4 theory in 4D

The one-component λφ 4 theory in four dimensions in the spontaneously broken symmetry phase has a non-trivial non-perturbative sector which can be studied by means of a duality transformation of its Ising limit. Duality maps this theory to a model of interacting membranes. Physical states correspond to membrane excitations. The way this non-perturbative behaviour can be reconciled with the triviality of the theory in its continuum limit is discussed.

Type IIB orientifolds, F-theory, Type I strings on orbifolds and Type I-heterotic duality

We consider six- and four-dimensional N = 1 supersymmetric orientifolds of Type IIB compactified on orbifolds. We give the conditions under which the perturbative world-sheet orientifold approach is adequate, and list the four-dimensional N = 1 orientifolds (which are rather constrained) that satisfy these conditions. We argue that in most cases orientifolds contain nonperturbative sectors that are missing in the world-sheet approach. These non-perturbative sectors can be thought of as arising from D-branes wrapping various collapsed 2-cycles in the orbifold. Using these observations, we explain certain “puzzles” in the literature on four-dimensional orientifolds. In particular, in some four-dimensional orientifolds the “naive” tadpole cancellation conditions have no solution. However, these tadpole cancellation conditions are derived using the world-sheet approach which we argue to be inadequate in these cases due to appearance of additional non-perturbative sectors. The main tools in our analyses are the map between F-theory and orientifold vacua and Type I-heterotic duality. Utilizing the consistency conditions we have found in this paper, we discuss consistent four-dimensional chiral N = 1 Type I vacua which are non-perturbative from the heterotic viewpoint.

Non-trivial behaviour of the scattering amplitude of contact-interacting anyons

It is shown that the scattering amplitude for contact-interacting anyons does exhibit a genuine non-perturbative sector. This means that the corresponding perturbative field theoretical formulation, based on the 2+1 non-relativistic Chern-Simons gauge model coupled to self-interacting complex scalar field, is not generally able to reproduce, order by order in perturbation theory, the exact result. It is proven that the full agreement between the exact scattering amplitude and the resummation of the perturbative expansion of the renormalized 1PI amplitude actually occurs only for some continuous sub-family of self-adjoint extensions of the quantum Hamiltonians, which entail the absence of bound states. A comparison with previously obtained results is carefully worked out.

Monopoles, Polyakov Loops, and Gauge Fixing on the Torus

We consider pure Yang–Mills theory on the four torus. A set of non-Abelian transition functions which encompass all instanton sectors is presented. It is argued that these transition functions are a convenient starting point for gauge fixing. In particular, we give an extended Abelian projection with respect to the Polyakov loop, whereA0is independent of time and in the Cartan subalgebra. In the non-perturbative sectors such gauge fixings are necessarily singular. These singularities can be restricted to Dirac strings joining monopole and anti-monopole like “defects”.

Correlations and multiplicity distributions in high energy collisions

In celebrating the 25 th anniversary of QCD, the theory of strong interactions, we focus our attention on the still standing problems of its non-perturbative sector using the advanced statistical methods and observables currently employed in multiparticle dynamics. In this paper we illustrate how H q oscillations and shoulder structure in e + e − annihilation are explained in terms of the superposition of 2- and 3-jet samples of events. Similar effects are also seen in the 2-jet sample of events and interpreted as the superposition of jets of different flavours. The elementary substructure in the two cases turns out to be a negative binomial distribution. It is proposed to interpret in the same way also H q oscillations and shoulder structure observed in hadron-hadron collisions.

The strange-quark mass from QCD sum rules in the pseudoscalar channel

QCD Laplace transform sum rules, involving the axial-vector current divergences, are used in order to determine the strange quark mass. The two-point function is known in QCD up to four loops in perturbation theory, and up to dimension-six in the non-perturbative sector. The hadronic spectral function is reconstructed using threshold normalization from chiral symmetry, together with experimental data for the two radial excitations of the kaon. The result for the running strange quark mass, in the MS scheme at a scale of 1 GeV 2 is: m ̄ s(1 GeV 2)=155±25 MeV .

A non-trivial spectrum for the trivial λΦ4 theory

It is pointed out that one-component Φ 4 theory in four dimensions has a non-perturbative sector that can be studied by means of an exact duality transformation of its Ising limit. This duality maps it to a membrane model. As a consequence, the Φ 4-theory turns out to have, in the broken symmetry phase, a remarkably rich spectrum of physical states corresponding to membrane excitations. A numerical study of the correlators between dual variables allows to evaluate the masses of the first few states.

Theμproblem andBandLconservation with a discrete gaugedRsymmetry

We examine in a generic context how the $\ensuremath{\mu}$ problem can be resolved by means of a spontaneously broken gauge symmetry. We then focus on the new scheme based on a discrete gauge $R$ symmetry which is spontaneously broken by nonperturbative hidden sector dynamics triggering supersymmetry breaking also. The possibility to suppress the dangerous baryon and/or lepton-number-violating interactions by means of this discrete $R$ symmetry is examined also together with some phenomenological consequences.

LIGHT-QUARK MESON SPECTROSCOPY

Light-quark meson spectroscopy provides a powerful tool for the study of QCD in the nonperturbative sector. There has been a lively experimental activity in this field over the last decade and different high-statistics results from large-acceptance spectrometer experiments have been published which have led to stimulating theoretical interpretations. Therefore it seems appropriate to review both the existing experimental results and the theoretical conclusions.

Introduction to QCD thermodynamics and the quark-gluon plasma

These lectures review recent theoretical work suggesting that hadronic matter may dissolve into a weakly interacting quark-gluon plasma phase at energy densities only one order of magnitude above the ground state energy density of nuclei. Basic techniques of field theory used for calculating thermodynamic properties of Quantum Chromodynamics (QCD) are introduced. Functional methods are applied to develop QCD perturbation theory at finite temperatures and chemical potentials. The relevance of asymptotic freedom at high T, μ is motivated. We then confront the main skeleton in the QCD closet, namely, the nonperturbative color magnetic sector. Techniques of lattice gauge theories to get beyond the limitations of perturbation theory are then discussed. Recent numerical results are critically assessed.