2023/03/17 by Joseph Ben Geloun, Geloun, Joseph Ben, Reiko Toriumi +1 · 1 citation
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2303.09829
Enhanced tensor field theories (eTFT) have dominant graphs that differ from the melonic diagrams of conventional tensor field theories. They therefore describe pertinent candidates to escape the so-called branched polymer phase, the universal geometry found for tensor models. For generic order d of the tensor field, we compute the perturbative β-functions at one-loop of two just-renormalizable quartic eTFT coined by + or ×, depending on their vertex weights. The models + has two quartic coupling constants (λ, λ+), and two 2-point couplings(mass, Za). Meanwhile, the model × has two quartic coupling constants (λ, λ×) and three 2-point couplings (mass, Za, Z2a). At all orders, both models have a constant wave function renormalization: Z=1 and therefore no anomalous dimension. Despite such peculiar behavior, both models acquire nontrivial radiative corrections for the coupling constants. The RG flow of the model + exhibits a particular asymptotic safety: λ+ is marginal without corrections thus is a fixed point of arbitrary constant value. All remaining couplings determine relevant directions and get suppressed in the UV. Concerning the model ×, λ× is marginal and again a fixed point (arbitrary constant value), λ, μ and Za are all relevant couplings and flow to 0. Meanwhile Z2a is a marginal coupling and becomes a linear function of the time scale. This model can neither be called asymptotically safe or free.