24,496 research outputs found
Large N Limit of Non-Commutative Gauge Theories
Using the correspondence between gauge theories and string theory in curved
backgrounds, we investigate aspects of the large limit of non-commutative
gauge theories by considering gravity solutions with fields. We argue that
the total number of physical degrees of freedom at any given scale coincides
with the commutative case. We then compute a two-point correlation function
involving momentum components in the directions of the -field. In the UV
regime, we find that the two-point function decays exponentially with the
momentum. A calculation of Wilson lines suggests that strings cannot be
localized near the boundary. We also find string configurations that are
localized in a finite region of the radial direction. These are worldsheet
instantons.Comment: 21 pages, harvmac. Some errors in correlators corrected, minor
corrections to the Lorentzian solution
Adaptive Mesh Refinement for Hyperbolic Systems based on Third-Order Compact WENO Reconstruction
In this paper we generalize to non-uniform grids of quad-tree type the
Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput.,
2001), thus obtaining a truly two-dimensional non-oscillatory third order
reconstruction with a very compact stencil and that does not involve
mesh-dependent coefficients. This latter characteristic is quite valuable for
its use in h-adaptive numerical schemes, since in such schemes the coefficients
that depend on the disposition and sizes of the neighboring cells (and that are
present in many existing WENO-like reconstructions) would need to be recomputed
after every mesh adaption.
In the second part of the paper we propose a third order h-adaptive scheme
with the above-mentioned reconstruction, an explicit third order TVD
Runge-Kutta scheme and the entropy production error indicator proposed by Puppo
and Semplice (Commun. Comput. Phys., 2011). After devising some heuristics on
the choice of the parameters controlling the mesh adaption, we demonstrate with
many numerical tests that the scheme can compute numerical solution whose error
decays as , where is the average
number of cells used during the computation, even in the presence of shock
waves, by making a very effective use of h-adaptivity and the proposed third
order reconstruction.Comment: many updates to text and figure
Remarks on the tensor degree of finite groups
The present paper is a note on the tensor degree of finite groups, introduced
recently in literature. This numerical invariant generalizes the commutativity
degree through the notion of nonabelian tensor square. We show two
inequalities, which correlate the tensor and the commutativity degree of finite
groups, and, indirectly, structural properties will be discussed.Comment: 5 pages; to appear with revisions in Filoma
Universality and Scaling at the Onset of Quantum Black Hole Formation
In certain two-dimensional models, collapsing matter forms a black hole if
and only if the incoming energy flux exceeds the Hawking radiation rate. Near
the critical threshold, the black hole mass is given by a universal formula in
terms of the distance from criticality, and there exists a scaling solution
describing the formation and evaporation of an arbitrarily small black hole.Comment: 9 pages, 3 figures (uuencoded
On Schwinger Pair Creation in Gravity and in Closed Superstring Theory
We investigate the Schwinger pair creation process in the context of
gravitational models with the back reaction of the electric field included in
the geometry. The background is also an exact solution of type II superstring
theory, where the electric field arises by Kaluza-Klein reduction. We obtain a
closed formula for the pair creation rate that incorporates the gravitational
back reaction. At weak fields it has the same structure as the general
Schwinger formula, albeit pairs are produced by a combination of Schwinger and
Unruh effect, the latter due to the presence of a Rindler horizon. In four
spacetime dimensions, the rate becomes constant at strong electric fields. For
states with mass of Kaluza-Klein origin, the rate has a power-like dependence
in the electric field, rather than the familiar (non-perturbative) exponential
dependence. We also reproduce the same formula from the string partition
function for winding string states. Finally, we comment on the generalization
to excited string states.Comment: 21 page
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