Duality of a Supersymmetric Standard Model

We examine a dual theory of a Supersymmetric Standard Model(SSM) in terms of an SU(3)C gauge group. In this scenario, it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the weak scale. Moreover, the supersymmetric Higgs mass parameter μ can naturally be expected to be small. This model automatically induces nine pairs of composite Higgs fields, which may be observed in the near future. e-mail: [email protected] Recently, it has become clear that certain aspects of four dimensional supersymmetric field theories can be analyzed exactly [1, 2, 3, 4]. One of the most interesting aspects is “duality” [1]. By using “duality”, we can infer the low energy effective theory of a strong coupling gauge theory. Does nature use this “duality”? In this paper, we would like to discuss a duality of a Supersymmetric Standard Model(SSM). First we would like to review Seiberg’s duality. Following his discussion [1], we examine SU(NC) supersymmetric (SUSY) QCD with NF flavors of chiral superfields, SU(NC) SU(NF )L SU(NF )R U(1)B U(1)R Q NC NF 1 1 (NF −NC)/NF Q̄j N̄C 1 N̄F −1 (NF −NC)/NF which has the global symmetry SU(NF )L ×SU(NF )R ×U(1)B ×U(1)R. This theory is called the electric theory. In the following, we would like to take NF ≥ NC +2, though in the case NF ≤ NC + 1 there are a lot of interesting features [3, 5, 6, 7]. Seiberg suggests [1] that in the case NF ≥ NC + 2 at the low energy scale the above theory is equivalent to the following SU(ÑC) SUSY QCD theory (ÑC = NF − NC) with NF flavors of chiral superfields qi and q̄ j and meson fields T i j , SU(ÑC) SU(NF )L SU(NF )R U(1)B U(1)R qi ÑC N̄F 1 NC/(NF −NC) NC/NF q̄ ̄̃ NC 1 NF −NC/(NF −NC) NC/NF T i j 1 NF N̄F 0 2(NF −NC)/NF and with a superpotential W = qiT i j q̄ j . (1) This theory is called the magnetic theory. The above two theories satisfy the ’t Hooft anomaly matching conditions [8]. Moreover Seiberg showed that they are consistent with the decoupling theorem [9]. Namely, if we introduce a mass term only for superfields QF and Q̄NF W = mQF Q̄NF (2) in the original (electric) theory, the dual (magnetic) theory has vacuum expectation values(VEVs) 〈q〉 = 〈q〉 = √m and SU(Nf −Nc) is broken to SU(Nf −Nc − 1), which is consistent with the decoupling of the heavy quark in the original theory.