Tensor field theory is the quantum field theoretic counterpart of tensor models. One may “enhance” certain interactions which are not of conventional melonic type so that they contribute to the dominant amplitudes, which consequently may drive us away from the branched polymer phase characterized by the usual melonic limit of tensor models. Therefore, such enhanced tensor field theories are of interest for the random geometric approach to quantum gravity. We consider two types of enhanced models + and × with order-d tensor fields ϕ : (U(1)D)d → ℂ and with the enhanced quartic interactions of the form p2aϕ4 reminiscent of derivative couplings expressed in momentum space. Scrutinising the degree of divergence via multiscale renormalization analysis, we study their renormalizability at all orders of perturbation. We furthermore compute the beta functions of the couplings to understand their renormalization group flow behaviour. At all orders of perturbation, both models have a constant wave function renormalisation, therefore no anomalous dimension. Despite such a peculiar behaviour, both models acquire non-trivial radiative corrections for the coupling constants. In particular, we observe in some of the coupling constants linear behaviour in the log of momentum.
This video was produced by the University of Münster, as part of the workshop From perturbative to non-perturbative QFT.
