Universality for polynomial invariants on ribbon graphs with half-ribbons

Avohou, Remi C.; Geloun, Joseph Ben; Hounkonnou, Mahouton Norbert

doi:10.48550/arxiv.1310.3708

Cited by 3 publications

(17 citation statements)

References 14 publications

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“…The new polynomial R found on HERGs then satisfies a contraction/cut recurrence relation. There exists another interesting operation on ribbon graphs which consists in moving the HRs on the boundary of these graphs [2]. It has been proved that one can quotient the action of these HR moves and get the so-called HR-equivalent classes of ribbon graphs with half-ribbons.…”

Section: Introductionmentioning

confidence: 99%

“…There exists a natural extension of R on these equivalence classes. The main result in [2] is the proof of the universal property of the polynomial R on HERGs and of its extension to HR-equivalent classes of ribbon graphs. This statement relies on the understanding and generalization of the tools necessary to the proof of the universality of the original BR polynomial.…”

Section: Introductionmentioning

confidence: 99%

“…In the present work which should be considered as a companion paper of [2], we will provide recipe theorems (Theorems 4 and 6) for computing any function F on HR-classes satisfying the contraction/cut rule from the knowledge of R. Our proof is then different from the one introduced in [10]. Indeed, the authors of this contribution based their proof on four items among which (item 2 therein) the factorization property of the BR polynomial when evaluated on one-pointjoint ribbon graphs.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is organized as follows. In section 2, we recall some results on the BR polynomial for HERGs and for HR-classes and its universality property obtained in [2]. The reader must be aware of the basics of ribbon graphs as found in [3] or [8] (but for notations closer to the present paper, we refer to [2]).…”

Section: Introductionmentioning

confidence: 99%

“…In section 2, we recall some results on the BR polynomial for HERGs and for HR-classes and its universality property obtained in [2]. The reader must be aware of the basics of ribbon graphs as found in [3] or [8] (but for notations closer to the present paper, we refer to [2]). In section 3, we give the first main result which is the proof of recipe theorems for this polynomial.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Recipe theorems for polynomial invariants on ribbon graphs with half-edges

Avohou¹,

Geloun²,

Hounkonnou³

2014

Preprint

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We provide recipe theorems for the Bollobàs and Riordan polynomial R defined on classes of ribbon graphs with half-edges introduced in arXiv:1310.3708[math.GT]. We also define a generalized transition polynomial Q on this new category of ribbon graphs and establish a relationship between Q and R. MSC(2010): 05C10, 57M15 Contents 1. Introduction 1 2. Polynomial invariants 2 3. Recipe theorems 9 4. Topological transition polynomial 15 Appendix 19 Appendix A. Recipe theorems for the polynomial on pinched ribbon graphs 19 Appendix B. One-point-joint and semi-factorization property of R 22 References 24

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Recipe theorems for polynomial invariants on ribbon graphs with half-edges

Avohou¹,

Geloun²,

Hounkonnou³

2014

Preprint

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The tensor track, III

Rivasseau

2013

Fortschritte der Physik

100

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We provide an informal up-to-date review of the tensor track approach to quantum gravity. In a long introduction we describe in simple terms the motivations for this approach. Then the many recent advances are summarized, with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion, Osterwalder-Schrader positivity...) which, while important for the tensor track program, are not detailed in the usual quantum gravity literature. We list open questions in the conclusion and provide a rather extended bibliography.

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Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term $\sum_{s}|p_s| + μ$

Geloun,

Toriumi

2014

Preprint

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We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank d Tensorial Group Field Theory. These models are called Abelian because their fields live on U (1) D . We concentrate on the case when these models are endowed with particular kinetic terms involving a linear power in momenta. New dimensional regularization and renormalization schemes are introduced for particular models in this class: a rank 3 tensor model, an infinite tower of matrix models φ 2n over U (1), and a matrix model over U (1) 2 . For all divergent amplitudes, we identify a domain of meromorphicity in a strip determined by the real part of the group dimension D. From this point, the ordinary subtraction program is applied and leads to convergent and analytic renormalized integrals. Furthermore, we identify and study in depth the Symanzik polynomials provided by the parametric amplitudes of generic rank d Abelian models. We find that these polynomials do not satisfy the ordinary Tutte's rules (contraction/deletion). By scrutinizing the "face"-structure of these polynomials, we find a generalized polynomial which turns out to be stable only under contraction.

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Universality for polynomial invariants on ribbon graphs with half-ribbons

Cited by 3 publications

References 14 publications

Recipe theorems for polynomial invariants on ribbon graphs with half-edges

Recipe theorems for polynomial invariants on ribbon graphs with half-edges

The tensor track, III

Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term $\sum_{s}|p_s| + μ$

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