104 research outputs found
Generalised Kinematics for Double Field Theory
We formulate a kinematical extension of Double Field Theory on a
-dimensional para-Hermitian manifold where the
metric is supplemented by an almost symplectic two-form
. Together and define an almost bi-Lagrangian structure
which provides a splitting of the tangent bundle
into two Lagrangian subspaces. In this paper a
canonical connection and a corresponding generalised Lie derivative for the
Leibniz algebroid on are constructed. We find integrability
conditions under which the symmetry algebra closes for general and
, even if they are not flat and constant. This formalism thus provides
a generalisation of the kinematical structure of Double Field Theory. We also
show that this formalism allows one to reconcile and unify Double Field Theory
with Generalised Geometry which is thoroughly discussed.Comment: 41 pages, v2: typos corrected, references added, published versio
Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
Boulatov and Ooguri have generalized the matrix models of 2d quantum gravity
to 3d and 4d, in the form of field theories over group manifolds. We show that
the Barrett-Crane quantum gravity model arises naturally from a theory of this
type, but restricted to the homogeneous space S^3=SO(4)/SO(3), as a term in its
Feynman expansion. From such a perspective, 4d quantum spacetime emerges as a
Feynman graph, in the manner of the 2d matrix models. This formalism provides a
precise meaning to the ``sum over triangulations'', which is presumably
necessary for a physical interpretation of a spin foam model as a theory of
gravity. In addition, this formalism leads us to introduce a natural
alternative model, which might have relevance for quantum gravity.Comment: 16 Pages (RevTeX), 4 eps figures. Minor revisions in the definition
of the mode
The 1/N expansion of colored tensor models
In this paper we perform the 1/N expansion of the colored three dimensional
Boulatov tensor model. As in matrix models, we obtain a systematic topological
expansion, with more and more complicated topologies suppressed by higher and
higher powers of N. We compute the first orders of the expansion and prove that
only graphs corresponding to three spheres S^3 contribute to the leading order
in the large N limit.Comment: typos corrected, references update
Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
We show how to properly gauge fix all the symmetries of the Ponzano-Regge
model for 3D quantum gravity. This amounts to do explicit finite computations
for transition amplitudes. We give the construction of the transition
amplitudes in the presence of interacting quantum spinning particles. We
introduce a notion of operators whose expectation value gives rise to either
gauge fixing, introduction of time, or insertion of particles, according to the
choice. We give the link between the spin foam quantization and the hamiltonian
quantization. We finally show the link between Ponzano-Regge model and the
quantization of Chern-Simons theory based on the double quantum group of SU(2)Comment: 48 pages, 15 figure
Colored Group Field Theory
Group field theories are higher dimensional generalizations of matrix models.
Their Feynman graphs are fat and in addition to vertices, edges and faces, they
also contain higher dimensional cells, called bubbles. In this paper, we
propose a new, fermionic Group Field Theory, posessing a color symmetry, and
take the first steps in a systematic study of the topological properties of its
graphs. Unlike its bosonic counterpart, the bubbles of the Feynman graphs of
this theory are well defined and readily identified. We prove that this graphs
are combinatorial cellular complexes. We define and study the cellular homology
of this graphs. Furthermore we define a homotopy transformation appropriate to
this graphs. Finally, the amplitude of the Feynman graphs is shown to be
related to the fundamental group of the cellular complex
Permutation combinatorics of worldsheet moduli space
52 pages, 21 figures52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published version52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published versio
Scalar-Tensor theories from Plebanski gravity
We study a modification of the Plebanski action, which generically
corresponds to a bi-metric theory of gravity, and identify a subclass which is
equivalent to the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories.
In this manner, scalar-tensor theories are displayed as constrained BF
theories. We find that in this subclass, there is no need to impose reality of
the Urbantke metrics, as also the theory with real bivectors is a scalar-tensor
theory with a real Lorentzian metric. Furthermore, while under the former
reality conditions instabilities can arise from a wrong sign of the scalar mode
kinetic term, we show that such problems do not appear if the bivectors are
required to be real. Finally, we discuss how matter can be coupled to these
theories. The phenomenology of scalar field dark matter arises naturally within
this framework.Comment: 21 page
- …