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

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. The resolution is that some vevs trigger marginal or irrelevant interactions, leading to Delta a=0 and decoupled dilaton on a subspace of the moduli space of vacua. This is contrary to classical intuition about Higgsing. This phenomenon often (but not always) correlates with negative R-charge for the Higgsing chiral operator.