482 research outputs found
Phase transitions of Large-N two-dimensional Yang-Mills and generalized Yang-Mills theories in the double scaling limit
The large-N behavior of Yang-Mills and generalized Yang-Mills theories in the
double-scaling limit is investigated. By the double-scaling limit, it is meant
that the area of the manifold on which the theory is defined, is itself a
function of N. It is shown that phase transitions of different orders occur,
depending on the functional dependence of the area on N. The finite-size
scalings of the system are also investigated. Specifically, the dependence of
the dominant representation on A, for large but finite N is determined.Comment: 11 pages, to appear in Eur. Phys. J.
Large-N limit of the two-dimensoinal Yang-Mills theory on surfaces with boundaries
The large-N limit of the two-dimensional U Yang-Mills theory on an
arbitrary orientable compact surface with boundaries is studied. It is shown
that if the holonomies of the gauge field on boundaries are near the identity,
then the critical behavior of the system is the same as that of an orientable
surface without boundaries with the same genus but with a modified area. The
diffenece between this effective area and the real area of the surface is
obtained and shown to be a function of the boundary conditions (holonomies)
only. A similar result is shown to hold for the group SU and other simple
groups.Comment: 11 pages, LaTeX2
-point functions of Yang-Mills theories on Riemann surfaces
Using the simple path integral method we calculate the -point functions of
field strength of Yang-Mills theories on arbitrary two-dimensional Riemann
surfaces. In case we show that the correlators consist of two parts , a
free and an -independent part. In the case of non-abelian semisimple compact
gauge groups we find the non-gauge invariant correlators in Schwinger-Fock
gauge and show that it is also divided to a free and an almost -independent
part. We also find the gauge-invariant Green functions and show that they
correspond to a free field theory.Comment: 8 pages,late
Large-N limit of the generalized 2D Yang-Mills theory on cylinder
Using the collective field theory approach of large-N generalized
two-dimensional Yang-Mills theory on cylinder, it is shown that the classical
equation of motion of collective field is a generalized Hopf equation. Then,
using the Itzykson-Zuber integral at the large-N limit, it is found that the
classical Young tableau density, which satisfies the saddle-point equation and
determines the large-N limit of free energy, is the inverse of the solution of
this generalized Hopf equation, at a certain point.Comment: 11 pages, add a paragraph after eq.(20) and add one reference,
accepted for publication in: Nucl. Phys. B (2000
Klein-Gordon and Dirac particles in non-constant scalar-curvature background
The Klein-Gordon and Dirac equations are considered in a semi-infinite lab
() in the presence of background metrics and with . These metrics have non-constant scalar-curvatures. Various aspects of the
solutions are studied. For the first metric with , it is shown
that the spectrums are discrete, with the ground state energy for spin-0 particles. For , the spectrums are
found to be continuous. For the second metric with , each
particle, depends on its transverse-momentum, can have continuous or discrete
spectrum. For Klein-Gordon particles, this threshold transverse-momentum is
, while for Dirac particles it is . There is no solution for
case. Some geometrical properties of these metrics are also
discussed.Comment: 14 pages, LaTeX, to be published in Int. Jour. Mod. Phys.
2-d Gravity as a Limit of the SL(2,R) Black Hole
The transformation of the black hole under a boost of the
subgroup U(1) is studied. It is found that the tachyon vertex operators of the
black hole go into those of the conformal field theory coupled to
gravity. The discrete states of the black hole also tend to the discrete states
of the 2-d gravity theory. The fate of the extra discrete states of the black
hole under boost are discussed.Comment: LaTeX file, 14 page
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