Non-Perturbative Defects in Tensor Models from Melonic Trees

Abstract

The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large $N$ limit known as the melonic limit that is strongly coupled yet solvable, producing at large distance a rare example of non-perturbative non-supersymmetric conformal field theory that admits analytic solutions. We study the dynamics of defects in the tensor model defined by localized magnetic field couplings on a $p$-dimensional subspace in the $d$-dimensional spacetime. While we work with general $p$ and $d$, the physically interesting cases include line defects in $d=2,3$ and surface defects in $d=3$. By identifying a novel large $N$ limit that generalizes the melonic limit in the presence of defects, we prove that the defect one-point function of the scalar field only receives contributions from a subset of the Feynman diagrams in the shape of melonic trees. These diagrams can be resummed using a closed Schwinger-Dyson equation which enables us to determine non-perturbatively this defect one-point function. At large distance, the solutions we find describe nontrivial conformal defects and we discuss their defect renormalization group (RG) flows. In particular, for line defects, we solve the exact RG flow between the trivial and the conformal lines in $d=4-\epsilon$. We also compute the exact line defect entropy and verify the $g$-theorem. Furthermore we analyze the defect two-point function of the scalar field and its decomposition via the operator-product-expansion, providing explicit formulae for one-point functions of bilinear operators and the stress-energy tensor.

47 pages, 10 figures

References in corpus (18)

• Generalized Global Symmetries
• Holography from Conformal Field Theory
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Entanglement Entropy, Trace Anomalies and Holography
• All point correlation functions in SYK
• The g-theorem and quantum information theory
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Instantons on the 5-sphere and M5-branes
• Irreversibility in quantum field theories with boundaries
• Symmetry Breaking in Coupled SYK or Tensor Models
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• 3d Abelian Gauge Theories at the Boundary
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• Boundary F-maximization
• Critical behavior in the presence of an order-parameter pinning field
• Line of fixed points in a bosonic tensor model
• Holography of 3d-3d correspondence at Large N
• The 1/2 BPS 't Hooft loops in N=4 SYM as instantons in 2d Yang-Mills