2004/08/31 by Edwin Barnes, Kenneth Intriligator, Ken Intriligator +2 · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2004.09.016
published as Nucl.Phys.B702:131-162,2004 · 36 pages, 6 figures. v2: added reference
arxiv created 2004/09/10 · openalex publication_date 2004/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 a-theorem, that aIR<aUV, using our result that the exact superconformal R-symmetry of 4d SCFTs maximizes a=3Tr R3-Tr R. The proof was incomplete because of two identified loopholes: theories with accidental symmetries, and the fact that it's only a local maximum of \ita. Here we discuss and extend a proposal of Kutasov (which helps close the latter loophole) in which a-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. a-maximization then yields a monotonically decreasing "a-function" along the RG flow to the IR. As we discuss, this proposal in fact suggests the strongest version of the a-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.