(Delta a) curiosities in some 4d susy RG flows

Understand

We explore some curiosities in 4d susy RG flows.

• One issue is that the compelling candidate a-function, from a-maximization with Lagrange multipliers, has a `strange branch," with reversed RG flow properties, monotonically increasing instead of decreasing.
• The branch flip to the strange branch occurs where a double-trace deformation Delta W=O ^2 passes through marginality, reminiscent of the condition for the chiral symmetry breaking, out of the conformal window transition in non-susy gauge theories.
• The second issue arises from Higgsing vevs for IR-free fields, which sometimes superficially violate the a-theorem.