2,892 research outputs found
The multivariate signed Bollobas-Riordan polynomial
We generalise the signed Bollobas-Riordan polynomial of S. Chmutov and I. Pak
[Moscow Math. J. 7 (2007), no. 3, 409-418] to a multivariate signed polynomial
Z and study its properties. We prove the invariance of Z under the recently
defined partial duality of S. Chmutov [J. Combinatorial Theory, Ser. B, 99 (3):
617-638, 2009] and show that the duality transformation of the multivariate
Tutte polynomial is a direct consequence of it.Comment: 17 pages, 2 figures. Published version: a section added about the
quasi-tree expansion of the multivariate Bollobas-Riordan polynomia
Renormalization of the Orientable Non-commutative Gross-Neveu Model
We prove that the non-commutative Gross-Neveu model on the two-dimensional
Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing,
renormalizability can be achieved. However, in the massive case, this forces us
to introduce an additional counterterm of the form "psibar i gamma^{0}
gamma^{1} psi". The massless case is renormalizable without such an addition.Comment: 45 pages, 5 figure
Hopf algebra of non-commutative field theory
We contruct here the Hopf algebra structure underlying the process of
renormalization of non-commutative quantum field theory.Comment: 14 pages, 4 figure
Quantum field theory on the degenerate Moyal space
We prove that the self-interacting scalar field on the four-dimensional
degenerate Moyal plane is renormalisable to all orders when adding a suitable
counterterm to the Lagrangean. Despite the apparent simplicity of the model, it
raises several non trivial questions. Our result is a first step towards the
definition of renormalisable quantum field theories on a non-commutative
Minkowski space.Comment: 21 pages, 4 figures. We use the techniques of the previous version in
a conclusive manner on the degenerate Moyal spac
Partial duality of hypermaps
We introduce a collection of new operations on hypermaps, partial duality,
which include the classical Euler-Poincar\'e dualities as particular cases.
These operations generalize the partial duality for maps, or ribbon graphs,
recently discovered in a connection with knot theory. Partial duality is
different from previous studied operations of S. Wilson, G. Jones, L. James,
and A. Vince. Combinatorially hypermaps may be described in one of three ways:
as three involutions on the set of flags (-model), or as three
permutations on the set of half-edges (-model in orientable case), or
as edge 3-colored graphs. We express partial duality in each of these models.Comment: 19 pages, 16 figure
Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
We study the polynomial Abelian or U(1)^d Tensorial Group Field Theories
equipped with a gauge invariance condition in any dimension d. From our
analysis, we prove the just renormalizability at all orders of perturbation of
the phi^4_6 and phi^6_5 random tensor models. We also deduce that the phi^4_5
tensor model is super-renormalizable.Comment: 33 pages, 22 figures. One added paragraph on the different notions of
connectedness, preciser formulation of the proof of the power counting
theorem, more general statements about traciality of tensor graph
Export and Innovation in Cambodian clothing manufacturing firms
Export and Innovation in Cambodian clothing manufacturing firm
Separability and the genus of a partial dual
Partial duality generalizes the fundamental concept of the geometric dual of
an embedded graph. A partial dual is obtained by forming the geometric dual
with respect to only a subset of edges. While geometric duality preserves the
genus of an embedded graph, partial duality does not. Here we are interested in
the problem of determining which edge sets of an embedded graph give rise to a
partial dual of a given genus. This problem turns out to be intimately
connected to the separability of the embedded graph. We determine how
separability is related to the genus of a partial dual. We use this to
characterize partial duals of graphs embedded in the plane, and in the real
projective plane, in terms of a particular type of separation of an embedded
graph. These characterizations are then used to determine a local move relating
all partially dual graphs in the plane and in the real projective plane
Topological graph polynomials and quantum field theory, Part II: Mehler kernel theories
We define a new topological polynomial extending the Bollobas-Riordan one,
which obeys a four-term reduction relation of the deletion/contraction type and
has a natural behavior under partial duality. This allows to write down a
completely explicit combinatorial evaluation of the polynomials, occurring in
the parametric representation of the non-commutative Grosse-Wulkenhaar quantum
field theory. An explicit solution of the parametric representation for
commutative field theories based on the Mehler kernel is also provided.Comment: 58 pages, 23 figures, correction in the references and addition of
preprint number
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