Abstract
We study the spectrum of the large quantum field theory of bosonic rank-3 tensors, the quartic interactions of which are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to determine the scaling dimensions of the bilinear operators of arbitrary spin. Using the fact that the theory is renormalizable in , we compare some of these results with the expansion, finding perfect agreement. This helps elucidate why the dimension of operator is complex for : the large fixed point in has complex values of the couplings for some of the invariant operators. We show that a similar phenomenon holds in the symmetric theory of a matrix field , where the double-trace operator has a complex coupling in dimensions. We also study the spectra of bosonic theories of rank- tensors with interactions. In dimensions , there is a critical value of , above which we have not found any complex scaling dimensions. The critical value is a decreasing function of , and it becomes 6 in . This raises a possibility that the large theory of rank-5 tensors with sextic potential has an IR fixed point which is free of perturbative instabilities for . This theory may be studied using renormalized perturbation theory in .
- Received 8 August 2017
DOI:https://doi.org/10.1103/PhysRevD.96.106014
© 2017 American Physical Society