Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 6, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP06(2020)065
Keywords
1; N Expansion; Renormalization Group
Categories
Funding
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program [818066]
- Spanish Research Agency (Agencia Estatal de Investigacion) through the grants IFT Centro de Excelencia Severo Ochoa [SEV-2016-0597, FPA2015-65480-P, PGC2018-095976-B-C21]
- Israeli Science Foundation Center of Excellence [2289/18]
- Quantum Universe I-CORE program of the Israel Planning and Budgeting Committee [1937/12]
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We study bosonic tensor field theories with sextic interactions in d < 3 dimensions. We consider two models, with rank-3 and rank-5 tensors, and U(N)(3) and O(N)(5) symmetry, respectively. For both of them we consider two variations: one with standard short-range free propagator, and one with critical long-range 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 rank-3 models admit melonic interacting fixed points, with real couplings and critical exponents: for the short-range model, we have a Wilson-Fisher fixed point with couplings of order root is an element of, in d = 3 - is an element of; for the long-range model, instead we have for any d < 3 a line of fixed points, parametrized by a real coupling g(1) (associated to the so-called 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 is an element of or small g(1).
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