Mapping Dirac gaugino masses

Abstract

We investigate the mapping of Dirac gaugino masses through regions of strong coupling, focussing on SQCD with an adjoint. These models have a well-known Kutasov duality, under which a weakly coupled electric UV description can flow to a different weakly coupled magnetic IR description. We provide evidence to show that Dirac gaugino mass terms map as lim μ→∞ m D gk 1 k+1 =lim μ→0 m ˜ D g ˜ k ˜ 1 k+1 under such a flow, where the coupling κ appears in the superpotential of the canonically normalised theory as W ⊃ κXk+1. This combination is an RG-invariant to all orders in perturbation theory, but establishing the mapping in its entirety is not straightforward because Dirac masses are not the spurions of holomorphic couplings in the N = 1 theory. To circumvent this, we first present evidence that deforming the Kutasov theory can make it flow to an N = 2 theory with parametrically small N = 1 deformations. This is shown to happen perturbatively in the weakly coupled theory, and we also identify the higgsing mechanism that has to take place in the dual theory. This is seen to occur correctly even when both theories are at strong coupling. Using harmonic superspace techniques we then identify the prepotential that can induce the same N = 1 deformations in the presence of electric and magnetic FI-terms. We show that the correct N = 1 scalar potential and fermion lagrangian are generated. It is then shown that pure Dirac mass terms can be induced by the same mechanism, and we find that the proposed RG-invariant is indeed preserved under N = 2 duality, and thence along the flow to the dual N = 1 Kutasov theories. Possible phenomenological applications are discussed.