Matching $A$ with $F$ in long-range QFTs (opens in new tab)

Unitarity is often a crucial ingredient in establishing theorems -- such as the $A$-theorem -- on the irreversibility of the renormalization group flow. The strongest thesis of this type of theorems would be that there exists a scalar function $A$ and a positive definite metric $G_{IJ}$ in the space of couplings such that the renormalization group flow satisfies a gradient equation, $\partial_I A= G_{IJ}\beta^J$, in which case $A$ is locally m...