Prismatic large N models for bosonic tensors

Abstract

We study the O(N ) 3 symmetric quantum field theory of a bosonic tensor φ abc with sextic interactions. Its large N limit is dominated by a positive-definite operator, whose index structure has the topology of a prism. We present a large N solution of the model using Schwinger-Dyson equations to sum the leading diagrams, finding that for 2.81 < d < 3 and for d < 1.68 the spectrum of bilinear operators has no complex scaling dimensions. We also develop perturbation theory in 3 − dimensions including eight O(N ) 3 invariant operators necessary for the renormalizability. For sufficiently large N , we find a "prismatic" fixed point of the renormalization group, where all eight coupling constants are real. The large N limit of the resulting expansions of various operator dimensions agrees with the Schwinger-Dyson equations. Furthermore, the expansion allows us to calculate the 1/N corrections to operator dimensions. The prismatic fixed point in 3 − dimensions survives down to N ≈ 53.65, where it merges with another fixed point and becomes complex. We also discuss the d = 1 model where our approach gives a slightly negative scaling dimension for φ, while the spectrum of bilinear operators is free of complex dimensions.

Hints of unitarity at large N in the O(N )3 tensor field theory

“…Tensor models can also be generalized in d dimensions to proper field theories. In this setting they give rise to a new family of conformal field theories (CFTs) at large N which are analytically accessible [38][39][40][41][42][43]. We call these conformal field theories melonic.…”

Supersymmetric tensor model at large N and small ε

“…In this section, we continue the investigation of the supersymmetric tensor model (1.1) from the point of view of the expansion. The calculation is similar to the ones performed in the papers [40,41,44]. We include all possible O(N ) 3 symmetric marginal interactions that respect the supersymmetry.…”

“…where we imposed a symmetry under the exchange of the colors. In comparison to the "prismatic" theory [41], which has 8 coupling constants, the supersymmetric theory has only 3; this is a significant simplification.…”

“…Such a "prismatic" theory was considered in the paper [41]. The solution of this theory was found in the large N limit and the RG properties were investigated at two loops.…”

Supersymmetric Landau-Ginzburg tensor models

“…There have also been serious attempts to find non-trivial IR fixed points in higher dimensional tensor models in the large N expansion [17,18]. Much of the analysis on this front has been carried out for bosonic models which generically suffer from an unbounded from below Hamiltonian.…”