Sextic tensor field theories in rank 3 and 5
Abstract
We study bosonic tensor field theories with sextic interactions in d < 3 dimensions. We consider two models, with rank3 and rank5 tensors, and U(N)^{3} and O(N)^{5} symmetry, respectively. For both of them we consider two variations: one with standard shortrange free propagator, and one with critical longrange propagator, such that the sextic interactions are marginal in any d < 3. We derive the set of beta functions at large N , compute them explicitly at four loops, and identify the respective fixed points. We find that only the rank3 models admit melonic interacting fixed points, with real couplings and critical exponents: for the shortrange model, we have a WilsonFisher fixed point with couplings of order √{ɛ }, in d = 3  ɛ; for the longrange model, instead we have for any d < 3 a line of fixed points, parametrized by a real coupling g_{1} (associated to the socalled wheel interaction). By standard conformal field theory methods, we then study the spectrum of bilinear operators associated to such interacting fixed points, and we find a real spectrum for small ɛ or small g_{1}.
 Publication:

Journal of High Energy Physics
 Pub Date:
 June 2020
 DOI:
 10.1007/JHEP06(2020)065
 arXiv:
 arXiv:1912.06641
 Bibcode:
 2020JHEP...06..065B
 Keywords:

 1/N Expansion;
 Renormalization Group;
 High Energy Physics  Theory
 EPrint:
 37 pages, v2: added some comments and figures, extended conclusions section, v3: corrected some numerical factors, qualitative results unchanged