Softly Broken SQCD: in the Continuum, on the Lattice, on the Brane

We analyze the possible soft breaking of $N=2$ supersymmetric Yang-Mills theory with and without matter flavour preserving the analyticity properties of the Seiberg-Witten solution. For small supersymmetry breaking parameter with respect to the dynamical scale of the theory we obtain an exact expression for the effective potential. We describe in detail the onset of the confinement transition and some of the patterns of chiral symmetry breaking. If we extrapolate the results ...

We study the dynamics of an 'electric' $\mathcal{N}=1$ 3D $U(N_c)_{k,k+\frac{N_c}{2}}$ SQCD theory. By embedding the theory in string theory, we propose that the theory admits a 'magnetic' dual and analyse the low energy dynamics of the theory using its dual. When $\frac{N_f}{2} \ge\frac{N_c}{2}-k$ the IR dynamics is described by either a TQFT for large quark masses, or a Grassmanian and a Wess-Zumino (WZ) term for small masses. We also consider non-supersymmetric mass deform...

We introduce a new supersymmetric extension of the standard model in which the gauge sector contains complete N=2 supersymmetry multiplets. Supersymmetry breaking from the D-term vev of a hidden sector U(1) gauge field leads to Dirac soft supersymmetry breaking gaugino masses, and a new type of soft scalar trilinear couplings. The resulting squark and slepton masses are finite, calculable, positive and flavor universal. The Higgs soft mass squared is negative. The phenomenolo...

The general SUSY soft breaking terms for a large class of phenomenologically relevant string scenarios (symmetric orbifolds) are given. They show a certain lack of universality, but not dangerous for flavor changing neutral currents. To get more quantitative results a specific SUSY breaking mechanism has to be considered, namely gaugino condensation in the hidden sector. Then, it turns out that squark and slepton masses tend to be much larger than scalar masses ($m_{\phi} > 1...

We calculate the soft SUSY breaking terms arising from a large class of string scenarios, namely symmetric orbifold constructions, and study its phenomenological viability. They exhibit a certain lack of universality, unlike the usual assumptions of the minimal supersymmetric standard model. Assuming gaugino condensation in the hidden sector as the source of SUSY breaking, it turns out that squark and slepton masses tend to be much larger than gaugino masses. Furthermore, we ...

We study the structure of soft breaking terms in the context of a gaugino condensation scenario. Assuming that the Supergravity Lagrangian is the correct quantum field theory limit, at some momentum scale $\mu_{UV}$, of a more fundamental one, we demonstrate that the correct result is obtained simply by substituting, in the tree level Supergravity Lagrangian, $\lambda \lambda$ (the gaugino condensate) by its vacuum expectation value $\Lambda^3$. In string inspired scenarios t...

After briefly reviewing the nonperturbative dynamics of N=1 supersymmetric field theories, soft SUSY breaking mass terms are introduced into the SUSY gauge theories and their effects on gauge symmetry breaking pattern are studied. For $N_f<N_c$, we include the dynamics of the non-perturbative superpotential and use the original (s)quark and gauge fields. For $N_f>N_c+1$, we formulate the dynamics in terms of dual (s)quarks and a dual gauge group SU(N_f-N_c). The mass squared ...

We analyze the effects of soft supersymmetry breaking terms on N=1 supersymmetric QCD with $N_f$ flavors and color gauge group $SU(N_c)$. The mass squared of some squarks may be negative, as long as vacuum stability is ensured by a simple mass inequality. For $N_f<N_c$, we include the dynamics of the non-perturbative superpotential and use the original (s)quark and gauge fields, while for $N_f>N_c+1$, we formulate the dynamics in terms of dual (s)quarks and a dual gauge group...

We revisit the study of confining vacua in the softly broken N=2 supersymmetric QCD, in the light of some recent developments in our understanding of the dynamics of N=2 gauge theories. These vacua are characterized by an effective magnetic $SU(r)$ gauge group ($0\leq r\leq N_f/2$) and are referred to sometimes as the $r$ vacua. We further clarify the meaning of $r \leftrightarrow N_{f}-r$ duality arising from the matching of semi-classical and quantum vacua. A particular att...

We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD to nonsupersymmetric models by adding soft supersymmetry breaking terms. In this way, we recover the standard vacuum of QCD with $N_f$ flavors and $N_c$ colors when $N_f < N_c$. However, for $N_f \geq N_c$, we find new exotic states---new vacua with spontaneously broken baryon number for $N_f = N_c$, and a vacuum state with unbroken chiral symmetry for $N_f > N_c$. These exotic vacua contain massles...