6 research outputs found
The complete 1/N expansion of colored tensor models in arbitrary dimension
In this paper we generalize the results of [1,2] and derive the full 1/N
expansion of colored tensor models in arbitrary dimensions. We detail the
expansion for the independent identically distributed model and the topological
Boulatov Ooguri model
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
Super-extended noncommutative Landau problem and conformal symmetry
A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an
arbitrary magnetic field, is considered, with particular attention paid to the
homogeneous case. The system has three different phases, depending on the
magnetic field. Due to supersymmetry, the boundary critical phase which
separates the sub- and super-critical cases can be viewed as a reduction to the
zero-energy eigensubspace. In the sub-critical phase the system is described by
the superextension of exotic Newton-Hooke symmetry, combined with the conformal
so(2,1) ~ su(1,1) symmetry; the latter is changed into so(3) ~ su(2) in the
super-critical phase. In the critical phase the spin degrees of freedom are
frozen and supersymmetry disappears.Comment: 12 pages, references added, published versio
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
Topological Graph Polynomials in Colored Group Field Theory
In this paper we analyze the open Feynman graphs of the Colored Group Field
Theory introduced in [arXiv:0907.2582]. We define the boundary graph
\cG_{\partial} of an open graph \cG and prove it is a cellular complex.
Using this structure we generalize the topological (Bollobas-Riordan) Tutte
polynomials associated to (ribbon) graphs to topological polynomials adapted to
Colored Group Field Theory graphs in arbitrary dimension