5,738 research outputs found
Two-logarithm matrix model with an external field
We investigate the two-logarithm matrix model with the potential
related to an exactly solvable
Kazakov-Migdal model. In the proper normalization, using Virasoro constraints,
we prove the equivalence of this model and the Kontsevich-Penner matrix model
and construct the 1/N-expansion solution of this model.Comment: 15pp., LaTeX, no figures, reference adde
Sedeonic relativistic quantum mechanics
We represent sixteen-component values "sedeons", generating associative
noncommutative space-time algebra. We demonstrate a generalization of
relativistic quantum mechanics using sedeonic wave functions and sedeonic
space-time operators. It is shown that the sedeonic second-order equation for
the sedeonic wave function, obtained from the Einstein relation for energy and
momentum, describes particles with spin 1/2. We show that for the special types
of wave functions the sedeonic second-order equation can be reduced to the set
of sedeonic first-order equations analogous to the Dirac equation. At the same
time it is shown that these sedeonic equations differ in space-time properties
and describe several types of massive and corresponding massless particles. In
particular we proposed four different equations, which could describe four
types of neutrinos.Comment: 22 pages, 3 table
Effective Action and Measure in Matrix Model of IIB Superstrings
We calculate an effective action and measure induced by the integration over
the auxiliary field in the matrix model recently proposed to describe IIB
superstrings. It is shown that the measure of integration over the auxiliary
matrix is uniquely determined by locality and reparametrization invariance of
the resulting effective action. The large-- limit of the induced measure for
string coordinates is discussed in detail. It is found to be ultralocal and,
thus, possibly is irrelevant in the continuum limit. The model of the GKM type
is considered in relation to the effective action problem.Comment: 9pp., Latex; v2: the discussion of the large N limit of the induced
measure is substantially expande
The MacMahon R-matrix
We introduce an -matrix acting on the tensor product of MacMahon
representations of Ding-Iohara-Miki (DIM) algebra
. This -matrix acts on pairs
of Young diagrams and retains the nice symmetry of the DIM algebra under
the permutation of three deformation parameters , and
. We construct the intertwining operator for a tensor product of
the horizontal Fock representation and the vertical MacMahon representation and
show that the intertwiners are permuted using the MacMahon -matrix.Comment: 39 page
Strategies of the level-by-level approach to the minimal route
The task of optimal path planning for drilling tool with numerical control is considered. Such tools are used in the production of printed circuit boards. The algorithm modification of level-by-level route construction for the approximate solution of the traveling salesman problem is discussed. Bypass objects can be specified either as a table of distances or values represented by a symmetric matrix, or as Cartesian coordinates (in applied cases of using numerically controlled equipment). The algorithm was tested on many different examples. As a result of the calculations performed for examples from the TSPLIB library (defined through a full distance matrix or Cartesian coordinates) with a dimension of up to 100 cities, the ability of the algorithm to construct the optimal route was confirmed. For examples from other sources or for artificially constructed ones (up to 130 objects), in the testing of the algorithm, the declared record values of the route minimum length were also achieved or improved. © 2019 ASTES Publishers. All rights reserved
BPS Monopole Equation in Omega-background
We study deformed supersymmetries in N=2 super Yang-Mills theory in the
Omega-backgrounds characterized by two complex parameters . When one of the -parameters vanishes, the theory has
extended supersymmetries. We compute the central charge of the algebra and
obtain the deformed BPS monopole equation. We examine supersymmetries preserved
by the equation.Comment: 14 pages, typos corrected, published version in JHE
Generalized matrix models and AGT correspondence at all genera
We study generalized matrix models corresponding to n-point Virasoro
conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT
correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge
theories with generalized quiver diagrams. We obtain the generalized matrix
models from the perturbative evaluation of the Liouville correlation functions
and verify the consistency of the description with respect to degenerations of
the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2
gauge theory as the spectral curve of the generalized matrix model, thus
providing a check of AGT correspondence at all genera.Comment: 19 pages; v2: version to appear in JHE
Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge
theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev
matrix model (beta-ensemble) representations the latter being polylinear
combinations of Selberg integrals. The "pure gauge" limit of these matrix
models is, however, a non-trivial multiscaling large-N limit, which requires a
separate investigation. We show that in this pure gauge limit the Selberg
integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the
Nekrasov function for pure SU(2) theory acquires a form very much reminiscent
of the AMM decomposition formula for some model X into a pair of the BGW
models. At the same time, X, which still has to be found, is the pure gauge
limit of the elliptic Selberg integral. Presumably, it is again a BGW model,
only in the Dijkgraaf-Vafa double cut phase.Comment: 21 page
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