465 research outputs found
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
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
Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions
We study fermions coupled to Yang-Mills matrix models from the point of view
of emergent gravity. The matrix model Dirac operator provides an appropriate
coupling for fermions to the effective gravitational metric for general branes
with nontrivial embedding, albeit with a non-standard spin connection. This
generalizes previous results for 4-dimensional matrix models. Integrating out
the fermions in a nontrivial geometrical background induces indeed the
Einstein-Hilbert action of the effective metric, as well as additional terms
which couple the Poisson tensor to the Riemann tensor, and a dilaton-like term.Comment: 34 pages; minor change
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
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
Quantum Field Theory on the q-deformed Fuzzy Sphere
We discuss the second quantization of scalar field theory on the q-deformed
fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find
quantum field theories which are manifestly covariant under U_q(su(2)), have a
smooth limit q -> 1, and satisfy positivity and twisted bosonic symmetry
properties. Using a Drinfeld twist, they are equivalent to ordinary but
slightly "nonlocal" QFT's on the undeformed fuzzy sphere, which are covariant
under SU(2).Comment: 8 pages, lecture given at the XXXVII Karpacz Winter School "New
Developments in Fundamental Interactions Theories" (February 6-15, 2000,
Karpacz, Poland). To be published in Proceeding
Gravity and compactified branes in matrix models
A mechanism for emergent gravity on brane solutions in Yang-Mills matrix
models is exhibited. Newtonian gravity and a partial relation between the
Einstein tensor and the energy-momentum tensor can arise from the basic matrix
model action, without invoking an Einstein-Hilbert-type term. The key
requirements are compactified extra dimensions with extrinsic curvature M^4 x K
\subset R^D and split noncommutativity, with a Poisson tensor \theta^{ab}
linking the compact with the noncompact directions. The moduli of the
compactification provide the dominant degrees of freedom for gravity, which are
transmitted to the 4 noncompact directions via the Poisson tensor. The
effective Newton constant is determined by the scale of noncommutativity and
the compactification. This gravity theory is well suited for quantization, and
argued to be perturbatively finite for the IKKT model. Since no
compactification of the target space is needed, it might provide a way to avoid
the landscape problem in string theory.Comment: 35 pages. V2: substantially revised and improved, conclusion
weakened. V3: some clarifications, published version. V4: minor correctio
A nontrivial solvable noncommutative \phi^3 model in 4 dimensions
We study the quantization of the noncommutative selfdual \phi^3 model in 4
dimensions, by mapping it to a Kontsevich model. The model is shown to be
renormalizable, provided one additional counterterm is included compared to the
2-dimensional case which can be interpreted as divergent shift of the field
\phi. The known results for the Kontsevich model allow to obtain the genus
expansion of the free energy and of any n-point function, which is finite for
each genus after renormalization. No coupling constant or wavefunction
renormalization is required. A critical coupling is determined, beyond which
the model is unstable. This provides a nontrivial interacting NC field theory
in 4 dimensions.Comment: 24 pages, 2 figures. V2: typos fixe
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