Vector Beta function

Understand

We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories.

• We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like relation among anomalous dimensions and a gradient property.
• We further conjecture that non-renormalization holds if and only if the vector operator is conserved.
• The local renormalization group analysis guarantees the first three within power counting renormalization.