Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$

Abstract

We study fixed-points of scalar fields that transform in the bifundamental representation of $O(N)\times O(M)$ in $3-\epsilon$ dimensions, generalizing the classic tricritical sextic vector model. In the limit where $N$ is large but $M$ is finite, we determine the complete beta function to order $1/N$ for arbitrary $M$. We find a rich collection of large-$N$ fixed-points in $d=3$, as well as fixed-points in $d=3-\epsilon$, that can be studied to all orders in the parameter $\hat{\epsilon }=N\epsilon$. With the goal of defining a large-$N$ nonsupersymmetric conformal field theory dominated by a web of planar diagrams, we also study fixed-points in the ``bifundamental'' large-$N$ limit, in which $M$ and $N$ are both large, but the ratio $M/N$ is held fixed. We find a unique infrared fixed-point in $d=3-\epsilon$, which we determine to order ${\epsilon }^2$. When $M/N\ll 1$, we also find an ultraviolet fixed-point in $d=3$ and $d=3-\epsilon$ that merges with the infrared fixed-point at $\epsilon \sim O(M/N)$. We expect at least one of two candidate fixed-points in integer dimensions -- the infrared fixed-point in $d=2$ and the ultraviolet fixed-point in $d=3$ -- to survive for finite values of $M/N$.

arXiv commentv2: 67 pages, 18 figures, accepted in Phys. Rev. D

References in corpus (43)

• The String Landscape, Black Holes and Gravity as the Weakest Force
• AdS Dual of the Critical O(N) Vector Model
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Higher Spin Gauge Theories: Star-Product and AdS Space
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Walking, Weak first-order transitions, and Complex CFTs
• Large Spin Perturbation Theory
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Analysis of Higher Spin Field Equations in Four Dimensions
• On Higher Spin Gauge Theory and the Critical O(N) Model
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Large-n Critical Behavior of O(n)xO(m) Spin Models
• Prismatic Large $N$ Models for Bosonic Tensors
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories
• A test of bosonization at the level of four-point functions in Chern-Simons vector models
• Critical O(N) model to order ${\epsilon }^4$ from analytic bootstrap
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Six-loop $\epsilon$ expansion study of three-dimensional $O(n)\times O(m)$ spin models
• Vacua Morghulis
• On the Light dilaton in the Large N Tri-critical O(N) Model
• Majorana Fermion Quantum Mechanics for Higher Rank Tensors
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Critical exponent omega at O(1/N) in O(N) x O(m) spin models
• Chiral exponents in O(N) x O(m) spin models at O(1/N^2)
• ABJ Quadrality
• The tri-fundamental quartic model
• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• Homoclinic RG flows, or when relevant operators become irrelevant
• Discovering and quantifying nontrivial fixed points in multi-field models
• Six dimensional Landau-Ginzburg-Wilson theory
• Sextic tensor model in rank $3$ at next-to-leading order
• Tensor Field Theories: Renormalization and Random Geometry