474 research outputs found
Fermions on spontaneously generated spherical extra dimensions
We include fermions to the model proposed in hep-th/0606021, and obtain a
renormalizable 4-dimensional SU(N) gauge theory which spontaneously generates
fuzzy extra dimensions and behaves like Yang-Mills theory on M^4 \times S^2. We
find a truncated tower of fermionic Kaluza-Klein states transforming under the
low-energy gauge group, which is found to be either SU(n), or SU(n_1) x SU(n_2)
x U(1). The latter case implies a nontrivial U(1) flux on S^2, leading to
would-be zero modes for the bifundamental fermions. In the non-chiral case they
may pair up to acquire a mass, and the emerging picture is that of mirror
fermions. We discuss the possible implementation of a chirality constraint in 6
dimensions, which is nontrivial at the quantum level due to the fuzzy nature of
the extra dimensions.Comment: 34 pages. V2: references added, minor corrections V3: discussion
added, final versio
Matrix Models, Emergent Gravity, and Gauge Theory
Matrix models of Yang-Mills type induce an effective gravity theory on
4-dimensional branes, which are considered as models for dynamical space-time.
We review recent progress in the understanding of this emergent gravity. The
metric is not fundamental but arises effectively in the semi-classical limit,
along with nonabelian gauge fields. This leads to a mechanism for protecting
certain geometries from corrections due to the vacuum energy.Comment: 8 pages. Based on invited talks given at the Conferences "Quantum
Spacetime and Noncommutative Geometry", Rome, 2008 and at "Workshop on
quantum gravity and nocommutative geometry", Lisbon, 2008 and at "Emergent
Gravity", Boston, 2008 and at DICE2008, Italy, 2008 and at "QG2 2008 Quantum
Geometry and Quantum Gravity", Nottingham, 200
Curvature and Gravity Actions for Matrix Models
We show how gravitational actions, in particular the Einstein-Hilbert action,
can be obtained from additional terms in Yang-Mills matrix models. This is
consistent with recent results on induced gravitational actions in these matrix
models, realizing space-time as 4-dimensional brane solutions. It opens up the
possibility for a controlled non-perturbative description of gravity through
simple matrix models, with interesting perspectives for the problem of vacuum
energy. The relation with UV/IR mixing and non-commutative gauge theory is
discussed.Comment: 17 pages; v2+v3: minor correction
Schwarzschild Geometry Emerging from Matrix Models
We demonstrate how various geometries can emerge from Yang-Mills type matrix
models with branes, and consider the examples of Schwarzschild and
Reissner-Nordstroem geometry. We provide an explicit embedding of these branes
in R^{2,5} and R^{4,6}, as well as an appropriate Poisson resp. symplectic
structure which determines the non-commutativity of space-time. The embedding
is asymptotically flat with asymptotically constant \theta^{\mu\nu} for large
r, and therefore suitable for a generalization to many-body configurations.
This is an illustration of our previous work arXiv:1003.4132, where we have
shown how the Einstein-Hilbert action can be realized within such matrix
models.Comment: 21 pages, 1 figur
Fuzzy Extra Dimensions: Dimensional Reduction, Dynamical Generation and Renormalizability
We examine gauge theories defined in higher dimensions where theextra
dimensions form a fuzzy (finite matrix) manifold. First we reinterpret these
gauge theories as four-dimensional theories with Kaluza-Klein modes and then we
perform a generalized \`a la Forgacs-Manton dimensional reduction. We emphasize
some striking features emerging in the later case such as (i) the appearance of
non-abelian gauge theories in four dimensions starting from an abelian gauge
theory in higher dimensions, (ii) the fact that the spontaneous symmetry
breaking of the theory takes place entirely in the extra dimensions and (iii)
the renormalizability of the theory both in higher as well as in four
dimensions. Then reversing the above approach we present a renormalizable four
dimensional SU(N) gauge theory with a suitable multiplet of scalar fields,
which via spontaneous symmetry breaking dynamically develops extra dimensions
in the form of a fuzzy sphere. We explicitly find the tower of massive
Kaluza-Klein modes consistent with an interpretation as gauge theory on , the scalars being interpreted as gauge fields on . Depending
on the parameters of the model the low-energy gauge group can be of the form
.Comment: 18 pages, Based on invited talks presented at various conferences,
Minor corrections, Acknowledgements adde
The 2D Continuum Radiative Transfer Problem: Benchmark Results for Disk Configurations
We present benchmark problems and solutions for the continuum radiative
transfer (RT) in a 2D disk configuration. The reliability of three Monte-Carlo
and two grid-based codes is tested by comparing their results for a set of
well-defined cases which differ for optical depth and viewing angle. For all
the configurations, the overall shape of the resulting temperature and spectral
energy distribution is well reproduced. The solutions we provide can be used
for the verification of other RT codes.We also point out the advantages and
disadvantages of the various numerical techniques applied to solve the RT
problem.Comment: 13 pages, 10 figures, To appear in Astronomy and Astrophysic
Emergent Geometry and Gravity from Matrix Models: an Introduction
A introductory review to emergent noncommutative gravity within Yang-Mills
Matrix models is presented. Space-time is described as a noncommutative brane
solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on
the brane arise as fluctuations of the bosonic resp. fermionic matrices around
such a background, and couple to an effective metric interpreted in terms of
gravity. Suitable tools are provided for the description of the effective
geometry in the semi-classical limit. The relation to noncommutative gauge
theory and the role of UV/IR mixing is explained. Several types of geometries
are identified, in particular "harmonic" and "Einstein" type of solutions. The
physics of the harmonic branch is discussed in some detail, emphasizing the
non-standard role of vacuum energy. This may provide new approach to some of
the big puzzles in this context. The IKKT model with D=10 and close relatives
are singled out as promising candidates for a quantum theory of fundamental
interactions including gravity.Comment: Invited topical review for Classical and Quantum Gravity. 57 pages, 5
figures. V2,V3: minor corrections and improvements. V4,V5: some improvements,
refs adde
Fuzzy Scalar Field Theory as a Multitrace Matrix Model
We develop an analytical approach to scalar field theory on the fuzzy sphere
based on considering a perturbative expansion of the kinetic term. This
expansion allows us to integrate out the angular degrees of freedom in the
hermitian matrices encoding the scalar field. The remaining model depends only
on the eigenvalues of the matrices and corresponds to a multitrace hermitian
matrix model. Such a model can be solved by standard techniques as e.g. the
saddle-point approximation. We evaluate the perturbative expansion up to second
order and present the one-cut solution of the saddle-point approximation in the
large N limit. We apply our approach to a model which has been proposed as an
appropriate regularization of scalar field theory on the plane within the
framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement
Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
We present a renormalizable 4-dimensional SU(N) gauge theory with a suitable
multiplet of scalar fields, which dynamically develops extra dimensions in the
form of a fuzzy sphere S^2. We explicitly find the tower of massive
Kaluza-Klein modes consistent with an interpretation as gauge theory on M^4 x
S^2, the scalars being interpreted as gauge fields on S^2. The gauge group is
broken dynamically, and the low-energy content of the model is determined.
Depending on the parameters of the model the low-energy gauge group can be
SU(n), or broken further to SU(n_1) x SU(n_2) x U(1), with mass scale
determined by the size of the extra dimension.Comment: 27 pages. V2: discussion and references added, published versio
- …