29 research outputs found
Singular topologies in the Boulatov model
Through the question of singular topologies in the Boulatov model, we
illustrate and summarize some of the recent advances in Group Field Theory.Comment: 4 pages; proceedings of Loops'11 (May 2011, Madrid); v2: minor
modifications matching published versio
Editorial for the special issue “progress in group field theory and related quantum gravity formalisms”
This editorial introduces the Special Issue “Progress in Group Field Theory and Related Quantum Gravity Formalisms” which includes a number of research and review articles covering results in the group field theory (GFT) formalism for quantum gravity and in various neighbouring areas of quantum gravity research. We give a brief overview of the basic ideas of the GFT formalism, list some of its connections to other fields, and then summarise all contributions to the Special Issue
Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization
Bubbles and jackets: new scaling bounds in topological group field theories
We use a reformulation of topological group field theories in 3 and 4
dimensions in terms of variables associated to vertices, in 3d, and edges, in
4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4
dimensions, we obtain a bubble bound proving the suppression of singular
topologies with respect to the first terms in the perturbative expansion (in
the cut-off). We also prove a new, stronger jacket bound than the one currently
available in the literature. We expect these results to be relevant for other
tensorial field theories of this type, as well as for group field theory models
for 4d quantum gravity.Comment: v2: Minor modifications to match published versio
Dirac-Born-Infeld-Volkov-Akulov and deformation of supersymmetry
We deform the action and the supersymmetry transformations of the d = 10 and d = 4 Maxwell supermultiplets so that at each order of the deformation the theory has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov type non-linear supersymmetries. The result agrees with the expansion in the string tension of the explicit action of the Dirac-Born-Infeld model and its supersymmetries, extracted from D9 and D3 superbranes, respectively. The half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new class of d = 6 vector branes related to chiral (2,0) supergravity, which we denote as 'Vp-branes'. We use a space-filling V5 superbrane for the d = 6 model and a V3 superbrane for the d = 4 half-maximal Dirac-Born-Infeld (DBI) models. In this way we present a completion to all orders of the deformation of the Maxwell supermultiplets with maximal 16+16 supersymmetries in d = 10 and 4, and half-maximal 8+8 supersymmetries in d = 6 and 4.</p
Functional renormalisation group approach for tensorial group field theory: a rank-3 model
Coarse graining methods for spin net and spin foam models
We undertake first steps in making a class of discrete models of quantum
gravity, spin foams, accessible to a large scale analysis by numerical and
computational methods. In particular, we apply Migdal-Kadanoff and Tensor
Network Renormalization schemes to spin net and spin foam models based on
finite Abelian groups and introduce `cutoff models' to probe the fate of gauge
symmetries under various such approximated renormalization group flows. For the
Tensor Network Renormalization analysis, a new Gauss constraint preserving
algorithm is introduced to improve numerical stability and aid physical
interpretation. We also describe the fixed point structure and establish an
equivalence of certain models.Comment: 39 pages, 13 figures, 1 tabl
Renormalizable Group Field Theory beyond melons: an example in rank four
We prove the renormalizability of a gauge-invariant, four-dimensional GFT model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case. The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself. This is possible because of the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms. This is one more instance of the peculiarity (and greater mathematical richness) of GFTs with respect to ordinary local quantum field theories. We also explore the renormalization group flow of the model at the non-perturbative level, using functional renormalization group methods, and identify a non-trivial fixed point in various truncations. This model is expected to have a similar structure of divergences as the GFT models of 4d quantum gravity, thus paving the way to more detailed investigations on them