Sextic tensor field theories in rank $3$ and $5$ - Archive ouverte HAL
Article Dans Une Revue Journal of High Energy Physics Année : 2020

Sextic tensor field theories in rank $3$ and $5$

Résumé

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 $ \sqrt{\epsilon } $, in d = 3 − ϵ; for the long-range model, instead we have for any d < 3 a line of fixed points, parametrized by a real coupling g$_{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 ϵ or small g$_{1}$.

Dates et versions

hal-02440024 , version 1 (14-01-2020)

Identifiants

Citer

Dario Benedetti, Nicolas Delporte, Sabine Harribey, Ritam Sinha. Sextic tensor field theories in rank $3$ and $5$. Journal of High Energy Physics, 2020, 06, pp.065. ⟨10.1007/JHEP06(2020)065⟩. ⟨hal-02440024⟩
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