Sextic tensor field theories in rank 3 and 5

DOI10.1007/JHEP06(2020)065zbMATH Open1437.81068arXiv1912.06641MaRDI QIDQ783871

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Publication date: 4 August 2020

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Abstract: 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 a 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 $sqrtepsilon$, in $d=3-epsilon$; 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 $epsilon$ or small $g_1$.

Full work available at URL: https://arxiv.org/abs/1912.06641

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