432 research outputs found
U(N) Gauge Theory and Lattice Strings
The U(N) gauge theory on a D-dimensional lattice is reformulated as a theory
of lattice strings (a statistical model of random surfaces). The Boltzmann
weights of the surfaces can have both signs and are tuned so that the
longitudinal modes of the string are elliminated. The U(\infty) gauge theory is
described by noninteracting planar surfaces and the 1/N corrections are
produced by surfaces with higher topology as well as by contact interactions
due to microscopic tubes, trousers, handles, etc. We pay special attention to
the case D=2 where the sum over surfaces can be performed explicitly, and
demonstrate that it reproduces the known exact results for the free energy and
Wilson loops in the continuum limit. In D=4 dimensions, our lattice string
model reproduces the strong coupling phase of the gauge theory. The weak
coupling phase is described by a more complicated string whose world surface
may have windows. A possible integration measure in the space of continuous
surfaces is suggested.Comment: 37 pages, 11 figures not included ; An extended version explaining in
addition the construction of the lattice string ansatz in D >2 dimensions.
(Note that the title has been changed.
Complex Curve of the Two Matrix Model and its Tau-function
We study the hermitean and normal two matrix models in planar approximation
for an arbitrary number of eigenvalue supports. Its planar graph interpretation
is given. The study reveals a general structure of the underlying analytic
complex curve, different from the hyperelliptic curve of the one matrix model.
The matrix model quantities are expressed through the periods of meromorphic
generating differential on this curve and the partition function of the
multiple support solution, as a function of filling numbers and coefficients of
the matrix potential, is shown to be the quasiclassical tau-function. The
relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed.
A general class of solvable multimatrix models with tree-like interactions is
considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of
J.Phys. A on Random Matrix Theor
Generalized Penner models to all genera
We give a complete description of the genus expansion of the one-cut solution
to the generalized Penner model. The solution is presented in a form which
allows us in a very straightforward manner to localize critical points and to
investigate the scaling behaviour of the model in the vicinity of these points.
We carry out an analysis of the critical behaviour to all genera addressing all
types of multi-critical points. In certain regions of the coupling constant
space the model must be defined via analytical continuation. We show in detail
how this works for the Penner model. Using analytical continuation it is
possible to reach the fermionic 1-matrix model. We show that the critical
points of the fermionic 1-matrix model can be indexed by an integer, , as it
was the case for the ordinary hermitian 1-matrix model. Furthermore the 'th
multi-critical fermionic model has to all genera the same value of
as the 'th multi-critical hermitian model. However, the
coefficients of the topological expansion need not be the same in the two
cases. We show explicitly how it is possible with a fermionic matrix model to
reach a multi-critical point for which the topological expansion has
alternating signs, but otherwise coincides with the usual Painlev\'{e}
expansion.Comment: 27 pages, PostScrip
The Color--Flavor Transformation of induced QCD
The Zirnbauer's color-flavor transformation is applied to the
lattice gauge model, in which the gauge theory is induced by a heavy chiral
scalar field sitting on lattice sites. The flavor degrees of freedom can
encompass several `generations' of the auxiliary field, and for each
generation, remaining indices are associated with the elementary plaquettes
touching the lattice site. The effective, color-flavor transformed theory is
expressed in terms of gauge singlet matrix fields carried by lattice links. The
effective action is analyzed for a hypercubic lattice in arbitrary dimension.
We investigate the corresponding d=2 and d=3 dual lattices. The saddle points
equations of the model in the large- limit are discussed.Comment: 24 pages, 6 figures, to appear in Int. J. Mod. Phys.
ДІАГНОСТИКА ЕНДОТЕЛІАЛЬНОЇ ДИСФУНКЦІЇ У ХВОРИХ НА АУТОІМУННИЙ ТИРЕОЇДИТ ЗА НАЯВНОСТІ АТЕРОСКЛЕРОТИЧНОГО УРАЖЕННЯ СУДИН
Поширеність аутоімунного тиреоїдиту(АІТ) в Україні за останні 10 років зросла на 68 %.АІТ є найчастішою причиною гіпотиреозу (70–80 % випадків). Ендотеліальна дисфункція (ЕД),що формується в умовах запального процесу, насьогодні розцінюється як основний патогенетич-ний чинник формування атеросклеротичногоураження судин, яке є морфологічною основоюішемічної хвороби серця (ІХС). Тому пошук пока-зових маркерів ЕД як при АІТ, так і при атероскле-розі (АС), є актуальним для оптимізації діагности-ки, оцінки перебігу та ефективності лікувальнихзаходів
Non-Perturbative Effects in Matrix Models and D-branes
The large order growth of string perturbation theory in conformal
field theory coupled to world sheet gravity implies the presence of
non-perturbative effects, whose leading behavior can be
calculated in the matrix model approach. Recently it was proposed that the same
effects should be reproduced by studying certain localized D-branes in
Liouville Field Theory, which were constructed by A. and Al. Zamolodchikov. We
discuss this correspondence in a number of different cases: unitary minimal
models coupled to Liouville, where we compare the continuum analysis to the
matrix model results of Eynard and Zinn-Justin, and compact c=1 CFT coupled to
Liouville in the presence of a condensate of winding modes, where we derive the
matrix model prediction and compare it to Liouville theory. In both cases we
find agreement between the two approaches. The c=1 analysis also leads to
predictions about properties of D-branes localized in the vicinity of the tip
of the cigar in SL(2)/U(1) CFT with c=26.Comment: 27 pages, lanlmac; minor change
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