Evidence for the strongest version of the 4d a-theorem via a-maximization along RG flows

In earlier work, we (KI and BW) gave a two line "almost proof" (for supersymmetric RG flows) of the weakest form of the conjectured 4d alpha-theorem, that alpha(IR) < alpha(UV), using our result that the exact superconformal R-symmetry of 4d SCFTs maximizes alpha = 3 Tr R-3 - Tr R. The proof was incomplete because of two identified loopholes: theories with accidental symmetries, and the fact that it is only a local maximum of alpha. Here we discuss and extend a proposal of Kutasov (which helps close the latter loophole) in which alpha-maximization is generalized away from the endpoints of the RG flow, with Lagrange multipliers that are conjectured to be identified with the running coupling constants. alpha-maximization then yields a monotonically decreasing "alpha-function" along the RG flow to the IR. As we discuss, this proposal in fact suggests the strongest version of the alpha-theorem: that 4d RG flows are gradient flows of an a-function, with positive-definite metric. In the perturbative limit, the RG flow metric thus obtained is shown to agree precisely with that found by very different computations by Osborn and collaborators. As examples, we discuss a new class of 4d SCFTs, along with their dual descriptions and IR phases, obtained from SQCD by coupling some of the flavors to added singlets. (C) 2004 Published by Elsevier B.V.