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

We consider $SU(N)$ $\mathcal{N}=4$ super Yang-Mills with cubic and quadratic soft SUSY breaking potential, such that the global $SU(4)_R$ is broken to $SU(3)$ or further. As shown recently, this set-up supports a rich set of non-trivial vacua with the geometry of self-intersecting $SU(3)$ branes in 6 extra dimensions. The zero modes on these branes can be interpreted as 3 generations of bosonic and chiral fermionic strings connecting the branes at their intersections. Here, ...

Effects of boundary conditions of fields for compactified space directions on the supersymmetric gauge theories are discussed. For general and possible boundary conditions the supersymmetry is explicitly broken to yield universal soft supersymmetry breaking terms, and the gauge symmetry of the theory can also be broken through the dynamics of non-integrable phases, depending on number and the representation under the gauge group of matters. The 4-dimensional supersymmetric QC...

We study a non-supersymmetric deformation of the field theory dual to the baryonic branch of Klebanov-Strassler. Using a combination of analytical (series expansions) and numerical methods we construct non-supersymmetric backgrounds that smoothly interpolate between the desired UV and IR behaviors. We calculate various observables of the field theory and propose a picture of soft breaking by gaugino masses that is consistent with the various calculations on the string side.

We give an explicit formalism connecting softly broken supersymmetric gauge theories (with QCD as one limit) to $N=2$ and $N=1$ supersymmetric theories possessing exact solutions, using spurion fields to embed these models in an enlarged $N=1$ model. The functional forms of effective Lagrangian terms resulting from soft supersymmetry breaking are constrained by the symmetries of the enlarged model, although not well enough to fully determine the vacuum structure of generic so...

We extend previous work on the soft breaking of $N=2$ supersymmetric QCD. We present the formalism for the breaking due to a dilaton spurion for a general gauge group and obtain the exact effective potential. We obtain some general features of the vacuum structure in the pure $SU(N)$ Yang-Mills theory and we also derive a general mass formula for this class of theories, in particular we present explicit results for the mass spectrum in the $SU(2)$ case. Finally we analyze the...

$\mathcal{N}=1$ supersymmetric QCD (SQCD) is a possible building block of theories beyond the standard model. It describes the interaction between gluons and quarks with their superpartners, gluinos and squarks. Since supersymmetry is explicitly broken by the lattice regularization, a careful fine-tuning of operators is necessary to obtain a supersymmetric continuum limit. For the pure gauge sector, $\mathcal{N}=1$ Supersymmetric Yang-Mills theory, supersymmetry is only broke...

We present a general analysis of all the possible soft breakings of N=2 supersymmetric QCD, preserving the analytic properties of the Seiberg-Witten solutions for the SU(2) group with Nf=1, 2, 3 hypermultiplets. We obtain all the couplings of the spurion fields in terms of properties of the Seiberg-Witten periods, which we express in terms of elementary elliptic functions by uniformizing the elliptic curves associated to each number of flavors. We analyze in detail the monodr...

We study softly broken N=1 supersymmetric QCD with the gauge group $SU(N_c)$ and $N_f$ flavours of quarks for $N_f > N_c+1$. We investigate the phase structure of its dual theory adding generic soft supersymmetry breking terms, i.e. soft scalar masses, trilinear coupling terms of scalar fields and gaugino masses. It is found that the trilinear coupling terms play an improtant role in determining the potential minima. Also we compare softly broken original and dual theories in...

Considered are ${\cal N}=2\, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ quark flavors with the quark mass term $m{\rm Tr}\,({\bar Q} Q)$ in the superpotential. ${\cal N}=2$ supersymmetry is softly broken down to ${\cal N}=1$ by the mass term $\mu_{\rm x}{\rm Tr}\,(X^2)$ of colored adjoint scalar partners of gluons, $\mu_{\rm x}\ll\Lambda_2$ ($\Lambda_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theori...

This paper could have been entitled "D branes and strings from flesh and blood." We study field theoretic prototypes of D branes/strings. To this end we consider (2+1)-dimensional domain walls in (3+1)-dimensional N=2 SQCD with SU(2) gauge group and two quark flavors in the fundamental representation. This theory is perturbed by a small mass term of the adjoint matter which, in the leading order in the mass parameter, does not break N=2 supersymmetry, and reduces to a (genera...