5,994 research outputs found
On the Origin of the UV-IR Mixing in Noncommutative Matrix Geometry
Scalar field theories with quartic interaction are quantized on fuzzy
and fuzzy to obtain the 2- and 4-point correlation functions at
one-loop. Different continuum limits of these noncommutative matrix spheres are
then taken to recover the quantum noncommutative field theories on the
noncommutative planes and respectively. The
canonical limit of large stereographic projection leads to the usual theory on
the noncommutative plane with the well-known singular UV-IR mixing. A new
planar limit of the fuzzy sphere is defined in which the noncommutativity
parameter , beside acting as a short distance cut-off, acts also as a
conventional cut-off in the momentum space. This
noncommutative theory is characterized by absence of UV-IR mixing. The new
scaling is implemented through the use of an intermediate scale that demarcates
the boundary between commutative and noncommutative regimes of the scalar
theory. We also comment on the continuum limit of the point function.Comment: Latex File, 3 Figure
String states, loops and effective actions in noncommutative field theory and matrix models
Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string
states as a tool for loop computations in noncommutative field theory and
matrix models. Defined in terms of coherent states, they exhibit the stringy
features of noncommutative field theory. This leads to a closed form for the
1-loop effective action in position space, capturing the long-range non-local
UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces.
The non-locality is tamed in the maximally supersymmetric IKKT or IIB model,
where it gives rise to supergravity. The linearized supergravity interactions
are obtained directly in position space at one loop using string states on
generic noncommutative branes.Comment: 31 pages, 2 figure
The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity
Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this
paper, I study numerically the fluctuation spectra around a Gaussian classical
solution of a tensor model, which represents a fuzzy flat space in arbitrary
dimensions. It is found that the momentum distribution of the low-lying
low-momentum spectra is in agreement with that of the metric tensor modulo the
general coordinate transformation in the general relativity at least in the
dimensions studied numerically, i.e. one to four dimensions. This result
suggests that the effective field theory around the solution is described in a
similar manner as the general relativity.Comment: 29 pages, 13 figure
Measuring the interactions among variables of functions over the unit hypercube
By considering a least squares approximation of a given square integrable
function by a multilinear polynomial of a specified
degree, we define an index which measures the overall interaction among
variables of . This definition extends the concept of Banzhaf interaction
index introduced in cooperative game theory. Our approach is partly inspired
from multilinear regression analysis, where interactions among the independent
variables are taken into consideration. We show that this interaction index has
appealing properties which naturally generalize the properties of the Banzhaf
interaction index. In particular, we interpret this index as an expected value
of the difference quotients of or, under certain natural conditions on ,
as an expected value of the derivatives of . These interpretations show a
strong analogy between the introduced interaction index and the overall
importance index defined by Grabisch and Labreuche [7]. Finally, we discuss a
few applications of the interaction index
Large-small dualities between periodic collapsing/expanding branes and brane funnels
We consider space and time dependent fuzzy spheres arising in
intersections in IIB string theory and collapsing D(2p)-branes in
IIA string theory.
In the case of , where the periodic space and time-dependent solutions
can be described by Jacobi elliptic functions, there is a duality of the form
to which relates the space and time dependent solutions.
This duality is related to complex multiplication properties of the Jacobi
elliptic functions. For funnels, the description of the periodic space
and time dependent solutions involves the Jacobi Inversion problem on a
hyper-elliptic Riemann surface of genus 3. Special symmetries of the Riemann
surface allow the reduction of the problem to one involving a product of genus
one surfaces. The symmetries also allow a generalisation of the to duality. Some of these considerations extend to the case of the
fuzzy .Comment: Latex, 50 pages, 2 figures ; v2 : a systematic typographical error
corrected + minor change
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
An equivalent condition to the Jensen inequality for the generalized Sugeno integral.
For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given
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