Abstract
We study two dimensional mathcal{N} = (2, 2) Landau-Ginzburg models with tensor valued superfields with the aim of constructing large central charge superconformal field theories which are solvable using large N techniques. We demonstrate the viability of such constructions and motivate the study of anisotropic tensor models. Such theories are a novel deformation of tensor models where we break the continuous symmetries while preserving the large N solvability. Specifically, we examine theories with superpotentials involving tensor contractions chosen to pick out melonic diagrams. The anisotropy is introduced by further biasing individual terms by different coefficients, all of the same order, to retain large N scaling. We carry out a detailed analysis of the resulting low energy fixed point and comment on potential applications to holography. Along the way we also examine gauged versions of the models (with partial anisotropy) and find generically that such theories have a non-compact Higgs branch of vacua.
Highlights
As is well known, large N field theories have played a key role in the holographic gauge/ gravity duality
We argue that the melonic diagrams still dominate in the large N limit as long as the anisotropic deformation parameters are chosen such that the coupling constants g αa1b1,a2b2,a3b3 are all of order
To mitigate issues arising from tensor valued bosonic field theories having Hamiltonians that are not bounded from below, we focused on theories with (2, 2) supersymmetry, where we can exploit non-renormalization theorems
Summary
Large N field theories have played a key role in the holographic gauge/ gravity duality. Even when one can stabilize the spectrum, by cleverly truncating a supersymmetric theory as in [19], the resulting fixed points often end up having operators violating unitarity bounds This intransigence of these models can in part be traced to the fact that while the Lagrangian may be engineered to only contain terms that give rise to melonic diagrams, renormalization effects induce non-tetrahedral tensor contractions (for example the so called pillow or double-sum terms). While these fail to produce moduli-free IR fixed points, there are several technical features of these models which we found to be interesting and unexplored in the literature (in particular, it is possible to construct moduli-free theories for small rank tensors). Appendix D has some further results regarding the gauged models for low rank theories
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