Double scaling in tensor models with a quartic interaction

Dartois, Stephane; Gurău, Razvan; Rivasseau, Vincent

doi:10.1007/jhep09(2013)088

Cited by 66 publications

(89 citation statements)

References 132 publications

(212 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, 2 Given a beta function βg = µ∂µg(µ), we can linearize it around a fixed point at g * : the RG will give meaningful results for the scaling exponent of the double-scaling limit even in cases where the expression for the partition function does not converge. In higher dimensions, there are indications that the partition function is summable in the double-scaling limit [20][21][22] and contributions from higher orders in the 1/N expansion [23] can be retained consistently. The FRG allows us to access tensor models corresponding to d = 4 dimensions, where other methods that work successfully in the matrix-model case, break down.…”

Section: A Renormalization Group and Double-scaling Limitmentioning

confidence: 99%

Towards phase transitions between discrete and continuum quantum spacetime from the renormalization group

Eichhorn

Koslowski

2014

Phys. Rev. D

View full text Add to dashboard Cite

We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the analysis of [1], we study three new aspects of the double-scaling limit of matrix models as Renormalization Group fixed points: Firstly, we investigate multicritical fixed points, which are associated with quantum gravity coupled to conformal matter. Secondly, we discuss an approximation that reduces the scheme dependence of our results as well as computational effort while giving good numerical results. This is a consequence of the approximation being a solution to the unitary Ward-identity associated to the U(N) symmetry of the hermitian matrix model. Thirdly, we discuss a scenario that relates the double scaling limit to fixed points of continuum quantum gravity.

show abstract

Section: A Renormalization Group and Double-scaling Limitmentioning

confidence: 99%

Towards phase transitions between discrete and continuum quantum spacetime from the renormalization group

Eichhorn

Koslowski

2014

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…Then the analyticity domain of A G extends to (61). The fact that the domain extends under the assumption (d) has a consequence for the same study now under the conditions (a) and (e).…”

Section: Theorem 1 (Extended Domain Of Analyticity) Consider a Tensomentioning

confidence: 70%

Parametric representation of rank d tensorial group field theory: Abelian models with kinetic term ∑sps+μ

Geloun

Toriumi

2015

Journal of Mathematical Physics

View full text Add to dashboard Cite

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.

show abstract

“…It is shown that the colored tensor models admit a large N expansion and the leading contributions represent higher dimensional sphere [26,27]. Moreover, it is claimed that one can take a double scaling limit in the tensor models [28,29]. Thus, the colored tensor models give a fascinating formulation of higher dimensional quantum gravity.…”

Section: Jhep07(2015)088mentioning

confidence: 99%

Random volumes from matrices

Fukuma

Sugishita

Umeda

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by semisimple associative algebras A. Although most of the diagrams represent configurations which are not manifolds, we show that the set of possible diagrams can be drastically reduced such that only (and all of the) three-dimensional manifolds with tetrahedral decompositions appear, by introducing a color structure and taking an appropriate large N limit. We examine the analytic properties when A is a matrix ring or a group ring, and show that the models with matrix ring have a novel strong-weak duality which interchanges the roles of triangles and hinges. We also give a brief comment on the relationship of our models with the colored tensor models.

show abstract

Double scaling in tensor models with a quartic interaction

Cited by 66 publications

References 132 publications

Towards phase transitions between discrete and continuum quantum spacetime from the renormalization group

Towards phase transitions between discrete and continuum quantum spacetime from the renormalization group

Parametric representation of rank d tensorial group field theory: Abelian models with kinetic term ∑sps+μ

Random volumes from matrices

Contact Info

Product

Resources

About