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Supersymmetric Landau-Ginzburg tensor models. (English) Zbl 1429.81064

Summary: 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.

MSC:

81T35 Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.)
81T60 Supersymmetric field theories in quantum mechanics
83E05 Geometrodynamics and the holographic principle
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

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