### Dmitri Diakonov - Research#

Prof. Dmitri Diakonov has made several pioneering contributions to the field of theoretical high energy physics and physics of elementary particles. He is a world
expert in the very difficult field of quantum field theory which has played, and still does,
the most prominent role in the field of theoretical particle physics.. In a nutshell, he is
particularly famous for his work on representation of Wilson loops as functional integrals over a group,
and on recognizing the role of instantons and other classical configurations in
the problem of confinement in quantum chromodynamics which is the standard model of strong interactions.

**More in detail:**

**1.** In the 1970’s Quantum Chromodynamics (QCD) has been formulated as a
candidate for the microscopic theory for strong (nuclear) interactions. However, at that time QCD seemed to
contradict many experimental observations. For example. it predicted violations
of Bjorken scaling in deep inelastic lepton scattering off nucleons, as well as the
growth of transverse momenta of outgoing particles with the overall momentum transfer. Neither was observed in
those early days.

Together with two graduate students Yu. Dokshitzer and S. Troian, Diakonov
undertook a systematic study of `hard' processes at high energies, i.e. those characterized
by high momentum transfer. Using clever tricks, they managed to sum up infinite
series of Feynman graphs in QCD, dominating in hard hadronic processes. They compared their results with
experiments, and proposed new experiments to check QCD directly. This was
a pioneering contribution to now booming field called `perturbative QCD’, helping to
establish the validity of QCD itself as the theory of strong interactions. This work enjoyes more
than thousand citations and is still used today.

**2.** In the beginning of the 1980’s Diakonov was one of the first to move
into then terra incognita of nonperturbative QCD. Most of physically important phenomena
in strong interactions like confinement of quarks, spontaneous chiral symmetry breaking
and breaking of the axial U(1) symmetry take place at strong coupling where perturbative
methods fail, hence the need for nonperturbative approaches.

Together with V. Petrov, Diakonov developed a new variational method for
gauge theories which they subsequently applied to build the `instanton liquid’ model of
the QCD vacuum state. [Instantons are certain large nonperturbative fluctuations of the
gluon field in the vacuum, of topological nature.] They obtained a self-consistent picture of a relatively dilute instanton ensemble, with all observables like the gluon condensate
or the topological susceptibility calculated - via the `transmutation of dimensions' - through
the basic Lambda parameter of QCD, and appearing in a fair agreement with the phenomenology.

A decade later, direct lattice simulations of the Yang-Mills vacuum have shown,
after certain `smearing' procedure, a distribution of instantons and anti-instantons
with the characteristics remarkably close to those variational estimates.

**3.** In 1984, Diakonov together with V. Petrov suggested a new microscopic
mechanism of spontaneous breaking of chiral symmetry in QCD. This is one
of the most, if not the most important phenomenon in strong interactions, manifesting
itself, in particular, in the fact that nucleons are heavy whereas pions are light.

The new mechanism was due to `hopping' of originally massless or nearly
massless quarks between instantons, or, to be more precise, as due to the delocalization
of the would-be zero fermion modes of individual instantons, in the ensemble of randomly spaced
and oriente instantons. Apart from being successful phenomenologically,
this work laid base for the application of the Random Matrix Theory to spontaneous chiral symmetry
breaking.

Diakonov’s papers on instantons have in total around two thousand citations.

**4.** In 1986 Diakonov and Petrov suggested a new field-theoretic model of
baryons named
`Chiral Quark--Soliton Model'. It was based on an earlier observation of
Diakonov and Eides
that integrating off quarks in the background pion field gave the Effective
Chiral Lagrangian
including the famous Wess – Zumino term and other four-derivatives terms
which proved to
desrcibe correctly the d-wave pion amplitudes and other observables. This
is the effective
theory to which full QCD is reduced at low momenta. The large number of
colours N_c is a
formal algebraic parameter justifying the use of a classical mean pion
field in the baryon
problem.

According to the model, baryons in the large-N_c limit can be viewed as
N_c `valence' quarks
bound by a self-consistent pion field whose energy is in fact coinciding
with the aggregate energy of the Dirac sea of quarks. The model interpolates between the Skyrme
model and the old non-relativistic quark models but contrary to the latter is field-theoretic and relativisticinvariant.

Therefore, it enables one to caclculate not only the static properties of baryons such as magnetic moments and axial constants but also the numerous parton distributions in
nucleons at a low normalization point, which are totally nonperturbative.

Using the Chiral Quark – Soliton Model, Diakonov and collaborators from Ruhr-Universitaet
Bochum calculated unpolarized and polarized quark and antiquark distributions
in nucleons. These distributions satisfy all general requirements (positivity, sum rules constraints,
etc.) and turn out to be in fair accordance with the phenomenology, without any `fitting'
parameters whatsoever.

This cycle of papers has more than thousand citations.

**5.** Basing on the above model in 1997 Diakonov (with V. Petrov and M. Polyakov)
predicted an existence of a relatively light and very narrow baryon resonance
with quantum
numbers that could be obtained only from four quarks and one antiquark
– an exotic
“pentaquark”, dubbed later on the Theta+ baryon by Diakonov.

This prediction stimulated a search of the Theta+ baryon by two independent
experimental
groups in Osaka in Moscow, and in the Autumn of 2002 both groups announced
strong
signals of the Theta+ precisely with the predicted mass, and very narrow.
That was followed
by a flow of a few dozen experiments at different installations worldwide,
and many hundreds
of theoretical papers.

Although the present experimental status of the Theta+ is still controversial,
this work by
Diakonov stimulated much activity in the study of hadron resonances and
in the search of new
ones, and played an important role in re-consideration of certain long-standing
prejudices in
the physics of strong interactions.

Recently, Diakonov gave a more intuitive explanation of the pentaquarks
in terms
of the mean-field approximation to baryon (justified theoretically at large
N_c), and predicted
a new type of pentaquarks containing heavy c or b quarks.

**6.** Quite recently Diakonov suggested a new microscopic mechanism of quark
conferment and
of the confinement-deconfinement phase transition at high temperatures,
based on the idea of
the dominance of monopole (dyon) configurations of the gluon field in the
ground state. The
quantum weight of dyons was computed for the first time by Diakonov and
collaborators,
which enabled him, together with Petrov, to build the statistical mechanics
of the ensemble of
interacting dyons, to which the Yang – Mills partition function reduces
in the semiclassical
approximation.

It was shown that the free energy of the quantum system of the Yang – Mills
fields had
the unique minimum corresponding to the zero average of the Polyakov line,
which is one of
the confinement criteria. All the other criteria – the area behaviour of
large Wilson loops, the
electric string appearing between static quarks, the disappearance of gluon
degrees of freedom
– where also demonstrated.

Furthermore, Diakonov showed that at higher temperatures, there is a competition
between
the dyons-induced nonperturbative free energy, and the perturbative one.
At certain critical
temperature T_c, the second prevails, and the system undergoes a phase
transition to the
deconfinement phase. The critical temperature computed in units of string
tension turns out to
be in remarkable agreement with lattice measurements of this quantity,
where available.