Chaotic RG flow in tensor models

Bosschaert, Maikel M.; Jepsen, Christian Baadsgaard; Popov, Fedor K.

doi:10.1103/physrevd.105.065021

Cited by 6 publications

(3 citation statements)

References 43 publications

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“…We explicitly found the conjugacy between R and the chaotic interval map and thus are able to analytically study the chaotic RG flow in the "coupling constant space," as is routinely done in standard RG treatments of physical systems. Incidentally, the fact that the RG flow of Haros graphs is conjugate to the shift map suggests some possible connection to spin systems with complex coupling constants, which were recently shown to possess a chaotic (Bernoulli) RG structure [6].…”

Section: Discussionmentioning

confidence: 99%

“…In the realm of condensed matter physics, Derrida and coauthors [3] showed that the appearance of unstable periodic orbits in the RG flow yields the onset of an infinite number of singularities in the free energy, i.e., the onset of an infinite number of critical temperatures. However, the quest for physical systems whose RG flow brings about a complex phase diagram has remained largely elusive, despite a few notable examples originating in quantum field theory [4][5][6] and condensed matter [7][8][9][10] (see also [11] and references therein for a recent example of a chaotic RG flow in a Potts model with long-range interactions). From a physical viewpoint, observing chaotic RG flow suggests that the system exhibits qualitatively different statistical behavior at different scales, a salient feature of, e.g., spin glasses.…”

Section: Introductionmentioning

confidence: 99%

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Chaotic renormalization group flow and entropy gradients over Haros graphs

2023

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Haros graphs have been recently introduced as a set of graphs bijectively related to real numbers in the unit interval. Here we consider the iterated dynamics of a graph operator R over the set of Haros graphs. This operator was previously defined in the realm of graph-theoretical characterization of low-dimensional nonlinear dynamics and has a renormalization group (RG) structure. We find that the dynamics of R over Haros graphs is complex and includes unstable periodic orbits of arbitrary period and nonmixing aperiodic orbits, overall portraiting a chaotic RG flow. We identify a single RG stable fixed point whose basin of attraction is associated with the set of rational numbers, and find periodic RG orbits that relate to (pure) quadratic irrationals and aperiodic RG orbits, related with (nonmixing) families of nonquadratic algebraic irrationals and transcendental numbers. Finally, we show that the graph entropy of Haros graphs is globally decreasing as the RG flows towards its stable fixed point, albeit in a strictly nonmonotonic way, and that such graph entropy remains constant inside the periodic RG orbit associated to a subset of irrationals, the so-called metallic ratios. We discuss the possible physical interpretation of such chaotic RG flow and put results regarding entropy gradients along RG flow in the context of c-theorems.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chaotic renormalization group flow and entropy gradients over Haros graphs

2023

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“…The RG equations are simply the system of first order ordinary differential equations defined by the beta function vector field on the space of couplings. While the beta functions can be calculated perturbatively from Feynman diagrams, as the RG equations represent perturbations in several parameters, the solutions are still potentially quite intricate [11].…”

Section: Jhep06(2024)108mentioning

confidence: 99%

Classifying large N limits of multiscalar theories by algebra

Flodgren,

Sundborg

2024

J. High Energ. Phys.

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We develop a new approach to RG flows and show that one-loop flows in multiscalar theories can be described by commutative but non-associative algebras. As an example related to D-brane field theories and tensor models, we study the algebra of a theory with M SU(N) adjoint scalars and its large N limits. The algebraic concepts of idempotents and Peirce numbers/Kowalevski exponents are used to characterise the RG flows. We classify and describe all large N limits of algebras of multiadjoint scalar models: the standard ‘t Hooft matrix theory limit, a ‘multi-matrix’ limit, each with one free parameter, and an intermediate case with extra symmetry and no free parameter of the algebra, but an emergent free parameter from a line of one-loop fixed points. The algebra identifies these limits without diagrammatic or combinatorial analysis.

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Boundary Liouville conformal field theory in four dimensions

Gaikwad,

Kislev,

Levy

et al. 2024

J. High Energ. Phys.

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Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary. We extend to the boundary, the conformally covariant GJMS operator and the $$ \mathcal{Q} $$ Q -curvature term in the LCFT action and classify the conformal boundary conditions. Working on a flat space with plate boundary, we calculate the dimensions of the boundary conformal primary operators, the two- and three-point functions of the displacement operator and the boundary conformal anomaly coefficients.

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Chaotic RG flow in tensor models

Cited by 6 publications

References 43 publications

Chaotic renormalization group flow and entropy gradients over Haros graphs

Chaotic renormalization group flow and entropy gradients over Haros graphs

Classifying large N limits of multiscalar theories by algebra

Boundary Liouville conformal field theory in four dimensions

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