The a-function in three dimensions: beyond leading order

Abstract

Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and shown to be related to the beta-functions by a gradient flow equation with positive-definite metric as in four dimensions. Here, we extend this lowest-order calculation to a general abelian Chern-Simons gauge theory coupled to fermions and scalars, and derive a prediction for part of the four-loop Yukawa beta-function. We also compute the complete four-loop Yukawa beta-function for the scalar-fermion theory and show that it is entirely consistent with the gradient flow equations at next-to-leading order.

24 pages; uses Axodraw. Revised version with typos corrected

References in corpus (34)

• On Renormalization Group Flows in Four Dimensions
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• The Exact Superconformal R-Symmetry Extremizes Z
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Chern-Simons Theory with Vector Fermion Matter
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• The Constraints of Conformal Symmetry on RG Flows
• The $a$-theorem and the Asymptotics of 4D Quantum Field Theory
• F-Theorem without Supersymmetry
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• The Thermal Free Energy in Large N Chern-Simons-Matter Theories
• Evidence for the Strongest Version of the 4d a-Theorem, via a-Maximization Along RG Flows
• On renormalization group flows and the a-theorem in 6d
• Constraints on RG Flow for Four Dimensional Quantum Field Theories
• Supersymmetric Chern-Simons Theories with Vector Matter
• Standard Model Vacuum Stability and Weyl Consistency Conditions
• Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
• New Results on the "$a$-theorem" in Four Dimensional Supersymmetric Field Theory
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• Generalized $F$-Theorem and the $\epsilon$ Expansion
• Lagrange Multipliers and Couplings in Supersymmetric Field Theory
• The a theorem for Gauge-Yukawa theories beyond Banks-Zaks
• RG flows in d dimensions, the dilaton effective action, and the a-theorem
• Structures on the Conformal Manifold in Six Dimensional Theories
• A challenge to the $a$-theorem in six dimensions
• Consequences of Weyl Consistency Conditions
• Consistency of local renormalization group in d=3
• Constructing a c-function for SUSY Gauge Theories
• The a-function for gauge theories
• Two-loop renormalization of multiflavor ${\varphi }^3$ theory in six dimensions and the trace anomaly
• The a-function in six dimensions
• Gradient flows in three dimensions
• Superconformal Chern-Simons theories beyond leading order
• Four-loop results for the anomalous dimension for a general N=2 supersymmetric Chern-Simons theory in three dimensions

Cited by in corpus (7)

• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• Anomalous dimensions for ${\varphi }^n$ in scale invariant $d=3$ theory
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• Scheme invariants in phi^4 theory in four dimensions
• The a-function for N=2 supersymmetric gauge theories in three dimensions
• Conformal Data of Fundamental Gauge-Yukawa Theories