Renormalizable enhanced tensor field theory: The quartic melonic case

Abstract

Tensor field theory is the quantum field theoretic counterpart of tensor models and enhanced tensor field theory enlarges this theory space to accommodate “enhanced tensor interactions.” These interactions were introduced to explore new large N limits and to probe different phases for tensor models. We undertake the multi-scale renormalization analysis for two types of enhanced theories with rank d tensor fields ϕ:(U(1)D)d→C and with the so-called quartic “melonic” interactions of the form p2aϕ4 reminiscent of derivative couplings expressed in momentum space. Scrutinizing the degree of divergence of both theories, we identify generic conditions for their renormalizability at all orders of perturbation at high momenta, i.e., the ultraviolet regime. For the first type of theory, we identify a 2-parameter space of just-renormalizable models for generic (d, D). These models have dominant non-melonic four-point functions. Finally, by specifying the parameters, we detail the renormalization analysis of the second type of model which is more exotic: it exhibits an infinite family of logarithmically divergent two-point amplitudes and all four-point amplitudes are convergent.