The Exact Superconformal R-symmetry Minimizes $τ_{RR}$

Details The Exact Superconformal R-symmetry Minimizes $τ_{RR}$ The Exact Superconformal R-symmetry Minimizes $τ_{RR}$

2005-07-14

arxiv.org/abs/hep-th/0507137v2

Nucl.Phys.B730:210-222,2005

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1016/j.nuclphysb.2005.10.003

We present a new, general constraint which, in principle, determines the superconformal $U(1)_R$ symmetry of 4d $\N =1$ SCFTs, and also 3d $\N =2$ SCFTs. Among all possibilities, the superconformal $U(1)_R$ is that which minimizes the coefficient, $\tau_{RR}$, of its two-point function. Equivalently, the superconformal $U(1)_R$ is the unique one with vanishing two-point function with every non-R flavor symmetry. For 4d $\N =1$ SCFTs, $\tau_{RR}$ minimization gives an alternative to a-maximization. $\tau_{RR}$ minimization also applies in 3d, where no condition for determining the superconformal $U(1)_R$ had been previously known. Unfortunately, this constraint seems impractical to implement for interacting field theories. But it can be readily implemented in the AdS geometry for SCFTs with AdS duals.

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