A New Anomaly Matching Condition?

Abstract

We formulate ``Witten'' matching conditions for confining gauge theories. The conditions are analogous to 't Hooft's, but involve Witten's global SU(2) anomaly. Using a group theoretic result of Geng, Marshak, Zhao and Okubo, we show that if the fourth homotopy group of the flavor group $H$ is trivial ($Π_4(H) = 0$) then realizations of massless composite fermions that satisfy the 't Hooft conditions also satisfy the Witten conditions. If $Π_4 (H)$ is nontrivial, the new matching conditions can yield additional information about the low energy spectrum of the theory. We give a simple physical proof of Geng, et. al.'s result.