997 research outputs found
Large-N limit of the two-dimensinal Non-Local Yang-Mills theory on arbitrary surfaces with boundary
The large-N limit of the two-dimensional non-local U Yang-Mills theory
on an orientable and non-orientable surface with boundaries is studied. For the
case which the holonomies of the gauge group on the boundaries are near the
identity, , it is shown that the phase structure of these theories
is the same as that obtain for these theories on orientable and non-orientable
surface without boundaries, with same genus but with a modified area
.Comment: 10 pages, no figure
Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories
In two-dimensional Yang-Mills and generalized Yang-Mills theories for large
gauge groups, there is a dominant representation determining the thermodynamic
limit of the system. This representation is characterized by a density the
value of which should everywhere be between zero and one. This density itself
is determined through a saddle-point analysis. For some values of the parameter
space, this density exceeds one in some places. So one should modify it to
obtain an acceptable density. This leads to the well-known Douglas-Kazakov
phase transition. In generalized Yang-Mills theories, there are also regions in
the parameter space where somewhere this density becomes negative. Here too,
one should modify the density so that it remains nonnegative. This leads to
another phase transition, different from the Douglas-Kazakov one. Here the
general structure of this phase transition is studied, and it is shown that the
order of this transition is typically three. Using carefully-chosen parameters,
however, it is possible to construct models with phase-transition orders not
equal to three. A class of these non-typical models are also studied.Comment: 11 pages, accepted for publication in Eur. Phys. J.
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Two-dimensional flux-corrected transport solver for convectively dominated flows
A numerical technique designed to solve a wide class of convectively dominated flow problems is presented. An attractive feature of the technique is its ability to resolve the behavior of field quantities possessing large gradients and/or shocks. The method is a finite-difference technique known as flux-corrected transport (FCT) that maintains four important numerical considerations - stability, accuracy, monotonicity, and conservation. The theory and methodology of two-dimensional FCT is presented. The method is applied in demonstrative example calculations of a 2-D Riemann problem with known exact solutions and to the Euler equations in a study of classical Rayleigh-Taylor and Kelvin-Helmholtz instability problems. The FCT solver has been vectorized for execution on the Cray 1S - a typical call with a 50 by 50 mesh requires about 0.00428 cpu seconds of execution time per call to the routine. Additionally, we have maintained a modular structure for the solver that eases its implementation. Fortran listings of two versions of the 2-D FCT solvers are appended with a driver main program illustrating the call sequence for the modules. 59 refs., 49 figs
Non-commutativity and Supersymmetry
We study the extent to which the gauge symmetry of abelian Yang-Mills can be
deformed under two conditions: first, that the deformation depend on a two-form
scale. Second, that the deformation preserve supersymmetry. We show that (up to
a single parameter) the only allowed deformation is the one determined by the
star product. We then consider the supersymmetry algebra satisfied by NCYM
expressed in commutative variables. The algebra is peculiar since the
supercharges are not gauge-invariant. However, the action, expressed in
commutative variables, appears to be quadratic in fermions to all orders in
theta.Comment: 21 pages, LaTeX; a reference adde
A Note on c=1 Virasoro Boundary States and Asymmetric Shift Orbifolds
We comment on the conformal boundary states of the c=1 free boson theory on a
circle which do not preserve the U(1) symmetry. We construct these Virasoro
boundary states at a generic radius by a simple asymmetric shift orbifold
acting on the fundamental boundary states at the self-dual radius. We further
calculate the boundary entropy and find that the Virasoro boundary states at
irrational radius have infinite boundary entropy. The corresponding open string
description of the asymmetric orbifold is given using the quotient algebra
construction. Moreover, we find that the quotient algebra associated with a
non-fundamental boundary state contains the noncommutative Weyl algebra.Comment: 21 pages, harvmac; v2: minor clarification in section 3.4; v3: a
discussion on cocycles added in section 2, and low energy limit mistake
removed and clarifications added in section 4.
The Spectrum of the Neumann Matrix with Zero Modes
We calculate the spectrum of the matrix M' of Neumann coefficients of the
Witten vertex, expressed in the oscillator basis including the zero-mode a_0.
We find that in addition to the known continuous spectrum inside [-1/3,0) of
the matrix M without the zero-modes, there is also an additional eigenvalue
inside (0,1). For every eigenvalue, there is a pair of eigenvectors, a
twist-even and a twist-odd. We give analytically these eigenvectors as well as
the generating function for their components. Also, we have found an
interesting critical parameter b_0 = 8 ln 2 on which the forms of the
eigenvectors depend.Comment: 25+1 pages, 3 Figures; typos corrected and some comments adde
Character Expansion Methods for Matrix Models of Dually Weighted Graphs
We consider generalized one-matrix models in which external fields allow
control over the coordination numbers on both the original and dual lattices.
We rederive in a simple fashion a character expansion formula for these models
originally due to Itzykson and Di Francesco, and then demonstrate how to take
the large N limit of this expansion. The relationship to the usual matrix model
resolvent is elucidated. Our methods give as a by-product an extremely simple
derivation of the Migdal integral equation describing the large limit of
the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a
number of models solvable by traditional means. We then proceed to solve a new
model: a sum over planar graphs possessing even coordination numbers on both
the original and the dual lattice. We conclude by formulating equations for the
case of arbitrary sets of even, self-dual coupling constants. This opens the
way for studying the deep problem of phase transitions from random to flat
lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into
the text in Pictex commands. (Two minor math typos corrected.
Acknowledgements added.
Non-commutative holography and scattering amplitudes in a large magnetic background
We study planar gluon scattering amplitudes and Wilson loops in
non-commutative gauge theory. Our main results are:
1. We find the map between observables in non-commutative gauge theory and
their holographic dual. In that map, the region near the boundary of the
gravitational dual describes the physics in terms of T-dual variables.
2. We show that in the presence of a large magnetic background and a UV
regulator, a planar gluon scattering amplitude reduces to a complex polygon
Wilson loop expectation value, dressed by a tractable polarization dependent
factor.Comment: 26 pages. v2: corrected section 4, reference adde
Open String Star as a Continuous Moyal Product
We establish that the open string star product in the zero momentum sector
can be described as a continuous tensor product of mutually commuting two
dimensional Moyal star products. Let the continuous variable parametrize the eigenvalues of the Neumann matrices; then the
noncommutativity parameter is given by .
For each , the Moyal coordinates are a linear combination of even
position modes, and the Fourier transform of a linear combination of odd
position modes. The commuting coordinate at is identified as the
momentum carried by half the string. We discuss the relation to Bars' work, and
attempt to write the string field action as a noncommutative field theory.Comment: 30 pages, LaTeX. One reference adde
Non-BPS Solutions of the Noncommutative CP^1 Model in 2+1 Dimensions
We find non-BPS solutions of the noncommutative CP^1 model in 2+1 dimensions.
These solutions correspond to soliton anti-soliton configurations. We show that
the one-soliton one-anti-soliton solution is unstable when the distance between
the soliton and the anti-soliton is small. We also construct time-dependent
solutions and other types of solutions.Comment: 11 pages, minor correction
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