1,721,090 research outputs found
Melonic CFTs
No full textInternational audienceThe melonic limit is a relatively new type of large- limit, differing from the much older and well-known large- limits of vector and matrix field theories, which are dominated by cactus and planar Feynman diagrams, respectively. The melonic limit typically appears in tensor field theories, characterized by an invariance group in which the fields transform as the product of fundamental representations of different simple Lie groups.As the name suggests, in such a limit the perturbative expansion of free energy and correlators are dominated by melonic diagrams. The latter form a manageable subset of the planar diagrams, but with a richer structure than cactus diagrams, and therefore they open the possibility of studying in a controlled manner new types of fixed points of the renormalization group. We call "melonic conformal field theories'' (CFTs) those fixed-point theories that are found in the melonic limit.We concisely review the construction and analysis of tensor field theories in (Euclidean) spacetime dimensions, with special emphasis on the general theoretical framework, and on specific results for the fixed points of some models
Melonic phase transition in group field theory
Full text linkGroup field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity
Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
No full textAbstractOrdinary tensor models of rank D≥3 are dominated at large N by tree-like graphs, known as melonic triangulations. We here show that non-melonic contributions can be enhanced consistently, leading to different types of large N limits. We first study the most generic quartic model at D=4, with maximally enhanced non-melonic interactions. The existence of the 1/N expansion is proved and we further characterize the dominant triangulations. This combinatorial analysis is then used to define a non-quartic, non-melonic class of models for which the large N free energy and the relevant expectations can be calculated explicitly. They are matched with random matrix models which contain multi-trace invariants in their potentials: they possess a branched polymer phase and a 2D quantum gravity phase, and a transition between them whose entropy exponent is positive. Finally, a non-perturbative analysis of the generic quartic model is performed, which proves analyticity in the coupling constants in cardioid domains
Tensor models with generalized melonic interactions
No full textInternational audienceTensor models are natural generalizations of matrix models. The interactions and observables in the case of unitary invariant models are generalizations of matrix traces. Some notable interactions in the literature include the melonic ones, the tetrahedral one as well as the planar ones in rank three, or necklaces in even ranks. Here we introduce generalized melonic interactions which generalize the melonic and necklace interactions. We characterize them as tree-like gluings of quartic interactions. We also completely characterize the Feynman graphs which contribute to the large limit. For a subclass of generalized melonic interactions called totally unbalanced interactions, we prove that the large limit is Gaussian and therefore the Feynman graphs are in bijection with trees. This result further extends the class of tensor models which fall into the Gaussian universality class. Another key aspect of tensor models with generalized melonic interactions is that they can be written as matrix models without increasing the number of degrees of freedom of the original tensor models. In the case of totally unbalanced interactions, this new matrix model formulation in fact decreases the number of degrees of freedom, meaning that some of the original degrees of freedom are effectively integrated. We then show how the large Gaussian behavior can be reproduced using a saddle point analysis on those matrix models
On melonic supertensor models
Full text linkAbstract We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large N limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for SL(2, ℝ) wavefunctions for fermionic excitations
Melonic limits of the quartic Yukawa model and general features of melonic CFTs
Full text linkWe study a set of large- tensor field theories with a rich structure of fixed points, encompassing both the melonic and prismatic CFTs observed previously in the conformal limits of other tensor theories and in the generalised Sachdev-Ye-Kitaev (SYK) model. The tensor fields interact via an -invariant generalisation of the quartic Yukawa model, . To understand the structure of IR/UV fixed points, we perform a partial four-loop perturbative analysis in . We identify the flows between the melonic and prismatic fixed points in the bosonic and fermionic sectors, finding an apparent line of fixed points in both. We reproduce these fixed points non-perturbatively using the Schwinger-Dyson equations, and in addition identify the supersymmetric fixed points in general dimension. Selecting a particular fermionic fixed point, we study its conformal spectrum non-perturbatively, comparing it to the sextic prismatic model. In particular, we establish the dimensional windows in which this theory remains stable. We comment on the structure of large- melonic CFTs across various dimensions, noting a number of features which we expect to be common to any such theory.48 pages + appendices, 16 figure
Melonic limits of the quartic Yukawa model and general features of melonic CFTs
Full text linkWe study a set of large-N tensor field theories with a rich structure of fixed points, encompassing both the melonic and prismatic CFTs observed previously in the conformal limits of other tensor theories and in the generalised Sachdev-Ye-Kitaev (SYK) model. The tensor fields interact via an O(N) 3 -invariant generalisation of the quartic Yukawa model, ϕ 2ψψ¯ +ϕ 6 . To understand the structure of IR/UV fixed points, we perform a partial four-loop perturbative analysis in D = 3 − ϵ. We identify the flows between the melonic and prismatic fixed points in the bosonic and fermionic sectors, finding an apparent line of fixed points in both. We reproduce these fixed points non-perturbatively using the Schwinger-Dyson equations, and in addition identify the supersymmetric fixed points in general dimension. Selecting a particular fermionic fixed point, we study its conformal spectrum non-perturbatively, comparing it to the sextic prismatic model. In particular, we establish the dimensional windows in which this theory remains stable. We comment on the structure of large-N melonic CFTs across various dimensions, noting a number of features which we expect to be common to any such theory
Melonic theories over diverse number systems
Full text linkMelonic field theories are defined over the p-adic numbers with the help of a sign character. Our construction works over the reals as well as the p-adics, and it includes the fermionic and bosonic Klebanov-Tarnopolsky models as special cases; depending on the sign character, the symmetry group of the field theory can be either orthogonal or symplectic. Analysis of the Schwinger-Dyson equation for the two-point function in the leading melonic limit shows that power law scaling behavior in the infrared arises for fermionic theories when the sign character is non-trivial, and for bosonic theories when the sign character is trivial. In certain cases, the Schwinger-Dyson equation can be solved exactly using a quartic polynomial equation, and the solution interpolates between the ultraviolet scaling controlled by the spectral parameter and the universal infrared scaling. As a by-product of our analysis, we see that melonic field theories defined over the real numbers can be modified by replacing the time derivative by a bilocal kinetic term with a continuously variable spectral parameter. The infrared scaling of the resulting two-point function is universal, independent of the spectral parameter of the ultraviolet theory
Melonic Large Limit of -Index Irreducible Random Tensors
No full textInternational audienceWe demonstrate that random tensors transforming under rank-5 irreducible representations of can support melonic large N expansions. Our construction is based on models with sextic (5-simplex) interaction, which generalize previously studied rank-3 models with quartic (tetrahedral) interaction (Benedetti et al. in Commun Math Phys 371:55, 2019. arXiv:1712.00249; Carrozza in JHEP 06:039, 2018. arXiv:1803.02496). Beyond the irreducible character of the representations, our proof relies on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs. Our results provide further evidence that the melonic limit is a universal feature of irreducible tensor models in arbitrary rank
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