Asymptotic freedom from the two loop term of the $\beta$-function in a cubic theory

Abstract

We renormalize a six dimensional cubic theory to four loops in the MSbar scheme where the scalar is in a bi-adjoint representation. The underlying model was originally derived in a problem relating to gravity being a double copy of Yang-Mills theory. As a field theory in its own right we find that it has a curious property in that while unexpectedly there is no one loop contribution to the $\beta$-function the two loop coefficient is negative. It therefore represents an example where asymptotic freedom is determined by the two loop term of the $\beta$-function. We also examine a multi-adjoint cubic theory in order to see whether this is a more universal property of these models.

arXiv comment17 latex pages

References in corpus (18)

• New Relations for Gauge-Theory Amplitudes
• The four-loop beta-function in Quantum Chromodynamics
• The three-loop QCD $\beta$-function and anomalous dimensions
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Connection between Feynman integrals having different values of the space-time dimension
• Gravity as the Square of Gauge Theory
• Reduze - Feynman Integral Reduction in C++
• Black holes and the double copy
• Group theory factors for Feynman diagrams
• The classical double copy for Taub-NUT spacetime
• The Multithreaded version of FORM
• Generalized Recurrence Relations for Two-loop Propagator Integrals with Arbitrary Masses
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Yang-Mills origin of gravitational symmetries
• A cubic action for self-dual Yang-Mills
• Biadjoint wires
• Regge behaviour and Regge trajectory for ladder graphs in scalar ${\Phi }^3$ field theory

Cited by in corpus (11)

• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Worldline description of a bi-adjoint scalar and the zeroth copy
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Remarks on a melonic field theory with cubic interaction
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• Renormalization group improvement of the effective potential in six dimensions
• Does our universe conform with the existence of a universal maximum energy-density ${\rho }_{max}^{uni}$ ?
• Resurgent Analysis of Ward-Schwinger-Dyson Equations
• Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term
• On kinetic theories with color and spin from amplitudes