157 research outputs found
Condensates and instanton - torus knot duality. Hidden Physics at UV scale
We establish the duality between the torus knot superpolynomials or the
Poincar\'e polynomials of the Khovanov homology and particular condensates in
-deformed 5D supersymmetric QED compactified on a circle with 5d
Chern-Simons(CS) term. It is explicitly shown that -instanton contribution
to the condensate of the massless flavor in the background of four-observable,
exactly coincides with the superpolynomial of the torus knot where
- is the level of CS term. In contrast to the previously known results, the
particular torus knot corresponds not to the partition function of the gauge
theory but to the particular instanton contribution and summation over the
knots has to be performed in order to obtain the complete answer. The
instantons are sitting almost at the top of each other and the physics of the
"fat point" where the UV degrees of freedom are slaved with point-like
instantons turns out to be quite rich. Also also see knot polynomials in the
quantum mechanics on the instanton moduli space. We consider the different
limits of this correspondence focusing at their physical interpretation and
compare the algebraic structures at the both sides of the correspondence. Using
the AGT correspondence, we establish a connection between superpolynomials for
unknots and q-deformed DOZZ factors.Comment: v2: text substantially improve
RG-Whitham dynamics and complex Hamiltonian systems
Inspired by the Seiberg-Witten exact solution, we consider some aspects of
the Hamiltonian dynamics with the complexified phase space focusing at the
renormalization group(RG)-like Whitham behavior. We show that at the
Argyres-Douglas(AD) point the number of degrees of freedom in Hamiltonian
system effectively reduces and argue that anomalous dimensions at AD point
coincide with the Berry indexes in classical mechanics. In the framework of
Whitham dynamics AD point turns out to be a fixed point. We demonstrate that
recently discovered Dunne-\"Unsal relation in quantum mechanics relevant for
the exact quantization condition exactly coincides with the Whitham equation of
motion in the Omega - deformed theory.Comment: v3: 34 pages, several typos corrected, a reference added, to appear
in Nuclear Physics
On an exact hydrodynamic solution for the elliptic flow
Looking for the underlying hydrodynamic mechanisms determining the elliptic
flow we show that for an expanding relativistic perfect fluid the transverse
flow may derive from a solvable hydrodynamic potential, if the entropy is
transversally conserved and the corresponding expansion "quasi-stationary",
that is mainly governed by the temperature cooling. Exact solutions for the
velocity flow coefficients and the temperature dependence of the spatial
and momentum anisotropy are obtained and shown to be in agreement with the
elliptic flow features of heavy-ion collisions.Comment: 10 pages, 4 figure
Particle Freeze-out and Discontinuities in Relativistic Hydrodynamics
Freeze-out of particles in relativistic hydrodynamics is considered across a
3-dimensional space-time hypersurface. The conservation laws for time-like
parts of the freeze-out hypersurface require different values of temperature,
baryonic chemical potential and flow velocity in the fluid and in the final
particle spectra. We analyze this freeze-out discontinuity and its connection
to the shock-wave phenomena in relativistic hydrodynamics.Comment: 6 figure
SOCIOLOGICAL MONITORING AS A TOOL FOR SOCIAL TENSION MEASUREMENT IN THE REGIONS MOST ATTRACTIVE FOR MIGRANTS
The application of social monitoring for the analysis of social tensions and ethnic conflicts prevention in the Russian regions that are most attractive for migrants are considered. The types of social contradictions, the occurrence of which may be due to the high attractiveness of the territory for migrants, both foreign and domestic, and provoke the emergence and increase of social tensions, - are described. The main determinants of social tension in the most attractive regions for migration are considered. It is noted that social tension is determined not only by ethnic and ethno-cultural characteristics of migrants, not typical for the population of the receiving community, but also by the contradictions between the economic interests of the local population and the economic interests of migrants
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