Approaching Continuum Geometry Dynamically: The Full Large-N Phase Space of Melonic Interactions

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Abstract

Tensor models provide generating functions for various classes of higher-dimensional triangulations with interesting continuum geometries at (multi)critical points. However, these geometries fall in the same universality classes already known from matrix models. One way to broaden the framework is to consider the tensor indices as dynamical, propagating degrees of freedom in a field theory. This allows to find new critical behaviour at fixed points of the renormalization group flow.  The potential of such tensor theories has not been fully exploited yet since only a symmetry-reduced ``isotropic'' part of their phase space has been studied so far. In this talk, I will show how applying the functional renormalization group to tensor fields in the full, anisotropic cyclic-melonic potential approximation unveals a plethora of new non-Gaussian fixed points. These fixed points correspond to continuum limits of distinguished ensembles of triangulations raising hope to find new classes of continuum geometry in this way. This talk is based on arxiv.org/abs/2406.01368 with Leonardo Juliano.

Speakers from the University of Münster

Thürigen, Johannes

Professur für Reine Mathematik (Prof. Wulkenhaar)