Implication of Exact SUSY Gauge Couplings for QCD

The phase structure of SUSY gauge theories can be very different from their nonsupersymmetric counterparts. Nonetheless, there is interesting information which might be gleaned from detailed investigation of these theories. In particular, we study the precise meaning of the strong interaction scale $\mathrm{\Lambda }$. We ask whether one can meaningfully apply naive dimensional analysis and also ask whether the study of supersymmetric theories can shed light on the apparent discrepancy between the perturbative scale ${\mathrm{\Lambda }}_{QCD}$ and the chiral lagrangian'' scale $\Lambda_\chi$. We show that in N=1 supersymmetric Yang Mills theory, naive dimensional analysis’’ seems to work well, with ${\mathrm{\Lambda }}_{\chi }$ consistently equal to the scale at which the perturbatively evolved physical coupling becomes of order $4\pi$. We turn to N=2 theories to understand better the effect of instantons in accounting for the QCD discrepancy between scales. In N=2 supersymmetric SU(2) the instanton corrections are known to all orders from the Seiberg-Witten solution and give rise to a finite scale ratio between the scale at which the perturbatively evolved and ``nonperturbatively evolved’’ couplings blow up. Correspondingly, instanton effects are important even when the associated perturbatively evolved gauge coupling only gives $\alpha$ of order 1 (rather than $4\pi$). We compare the N=2 result to instanton-induced corrections in QCD, evaluated using lattice data and the instanton liquid model, and find a remarkably similar behavior.