The a-function for gauge theories

Abstract

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We construct the a-function at four loop order for a general gauge theory with fermions and scalars, using only one and two loop beta-functions; we are then able to provide a stringent consistency check on the general three-loop gauge beta-function. In the case of an N=1 supersymmetric gauge theory, we present a general condition on the chiral field anomalous dimension which guarantees an exact all-orders expression for the a-function; and we verify this up to fifth order (corresponding to the three-loop anomalous dimension).

28 pages; uses axodraw; typos corrected, also some sign errors corrected in Sect 5

References in corpus (6)

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Cited by in corpus (20)

• Vacuum stability of asymptotically safe gauge-Yukawa theories
• PyR@TE 3
• Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity
• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• Weyl Consistency Conditions and ${\gamma }_5$
• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• The a-function in six dimensions
• The Gauss-Bonnet Coupling Constant in Classically Scale-Invariant Gravity
• The a-function in three dimensions: beyond leading order
• Thermodynamics of asymptotically safe theories
• Scheme invariants in phi^4 theory in four dimensions
• Four-Fermion Limit of Gauge-Yukawa Theories
• The a-function for N=2 supersymmetric gauge theories in three dimensions
• Conformal Data of Fundamental Gauge-Yukawa Theories
• $\mathcal{N}=1$ Euler Anomaly Flow from Dilaton Effective Action
• Weyl Consistency Conditions from a local Wilsonian Cutoff
• Emergent Supersymmetry in the Marginal Deformations of N=4 SYM
• Gradient Flow and Holography from a Local Wilsonian Cutoff
• $\mathcal{N}$ = $1$ Euler Anomaly from RG-dependent metric-Background