3D Tensor Field Theory: Renormalization and One-Loop β-Functions

Geloun, Joseph Ben; Samary, Dine Ousmane

doi:10.1007/s00023-012-0225-5

Cited by 99 publications

(173 citation statements)

References 85 publications

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“…Moreover, many techniques may be applied to these field theories that are idiosyncratic to quantum field theories (as opposed to quantum mechanics). Perhaps the most striking is the study of their renormalisation group properties [208][209][210][211][212][213][214][215][216][217][218], but also work has commenced on the study of mean field theory properties [219], matter coupling [220][221][222], various symmetry analyses [223,224], and instantonic field theory solutions [225][226][227][228] (including cosmological applications [229]). …”

Section: Tensor Models and Tensor Group Field Theoriesmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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Section: Tensor Models and Tensor Group Field Theoriesmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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“…It turns out that Renormalization can be consistently defined for TGFTs and most of them, for the higher rank D ≥ 3 are UV asymptotically free [21]. This is of course very encouraging for the Geomeogenesis Scenario [15][23] [24].…”

Section: Introductionmentioning

confidence: 99%

Closed equations of the two-point functions for tensorial group field theory

Samary

2014

Class. Quantum Grav.

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In this paper we provide the closed equations that satisfy two-point correlation functions of the rank 3 and 4 tensorial group field theory. The formulation of the present problem extends the method used by Grosse and Wulkenhaar in [arXiv 0909.1389] to the tensor case. Ward-Takahashi identities and Schwinger-Dyson equations are combined to establish a nonlinear integral equation for the two-point functions. In the 3D case the solution of this equation is given perturbatively at second order of the coupling constant.Pacs numbers: 11.10. Gh,

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“…Thanks to recent breakthroughs in the closely related field of tensor models [18][19][20], the usual quantum field theory tools are currently being generalized to GFTs which increasingly resemble LQG. These developments include first and foremost perturbative renormalization [21][22][23][24][25][26][27][28], but also constructive results [29][30][31], and generalizations of the usual functional renormalization group (FRG) methods [32,33].…”

Section: Introductionmentioning

confidence: 99%

Group field theory in dimension4−ϵ

Carrozza

2015

Phys. Rev. D

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Building on an analogy with ordinary scalar field theories, an ε-expansion for rank-3 tensorial group field theories with gauge invariance condition is introduced. This allows to continuously interpolate between the dimension four group SU(2) × U(1) and the dimension three SU(2). In the first situation, there is a unique marginal ϕ 4 coupling constant, but in contrast to ordinary scalar field theory this model is asymptotically free. In the SU(2) case, the presence of two marginally relevant ϕ 6 coupling constants and one ϕ 4 super-renormalizable interaction spoils this interesting property. However, the existence of a non-trivial fixed point is established in dimension 4 − ε, hence suggesting that the SU(2) theory might be asymptotically safe. To pave the way to future non-perturbative calculations, the present perturbative results are discussed in the framework of the effective average action.

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3D Tensor Field Theory: Renormalization and One-Loop β-Functions

Cited by 99 publications

References 85 publications

Spin Foam Models with Finite Groups

Spin Foam Models with Finite Groups

Closed equations of the two-point functions for tensorial group field theory

Group field theory in dimension4−ϵ

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