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

We discuss the introduction of soft breaking terms into the exact solutions of N=1 SQCD using a spurion analysis. The spurion symmetries are not sufficient to determine the behavior of models in which squark or gaugino masses alone are introduced. However, a controlled approximation is obtained in some cases if a supersymmetric mass is first introduced for the matter fields. We present low-energy solutions for two models with perturbing soft breaking terms, one with a gaugino...

We consider generic MQCD configurations with matter described by semi-infinte D4-branes and softly broken supersymmetry. We show that the matter sector does not introduce supersymmetry breaking parameters so that the most relevant supersymmetry breaking operator at low energies is the gaugino mass term. By studying the run-away properties of these models in the decoupling limit of the adjoint matter, we argue that these softly broken MQCD configurations fail to capture the in...

We analyze the theory of softly broken supersymmetric $QCD$. Exotic behavior like spontaneously broken baryon number, massless composite fermions and Seiberg's duality seems to persist also in the presence of (small) soft supersymmetry breaking. We argue that certain, specially tailored, lattice simulations may be able to detect the novel phenomena. Most of the exotic behavior does not survive the decoupling limit of large SUSY breaking parameters.

We embed the supersymmetry breaking mechanism in N=1 SQCD of hep-th/0602239 in a smooth superstring theory using D-branes in the background R^4 \times SL(2)_{k=1}/U(1) which smoothly captures the throat region of an intersecting NS5-brane configuration. A controllable deformation of the supersymmetric branes gives rise to the mass deformation of the magnetic SQCD theory on the branes. The consequent instability on the open string worldsheet can be followed onto a stable non-s...

Recently there have been proposals to understand features of QCD such as confinement and chiral symmetry breaking by considering supersymmetric versions of the theory with various patterns of soft breaking. In this note we recall that with small soft breakings, SUSY QCD is suggestive of observed features of real QCD. But we outline some of the challenges to establishing these features of the theory with large soft breakings. It appears difficult to argue for confinement or ch...

Supersymmetric Yang Mills theory is directly accessible to lattice simulations using current methodology, and can provide a non-trivial check of recent exact results in SQCD. In order to tune the lattice simulation to the supersymmetric point it is neccessary to understand the behavior of the theory with a small supersymmetry breaking gaugino mass. We introduce a soft breaking gaugino mass in a controlled fashion using a spurion analysis. We compute the gluino condensate, vac...

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. We present the formalism for an arbitrary gauge group and obtain an exact expression for the effective potential. We describe in detail the onset of the confinement description and the vacuum structure for the pure $SU(2)$ Yang-Mills case and also some general features in the $SU(N)$ case. A gener...

We identify the 4D field theories living on the world volume of D4 branes in non-supersymmetric type IIA string theory constructions. They are softly broken N=2 SQCD with the breakings introduced through vevs of the auxilliary fields in the spurion coupling field. Exact solutions of these theories for perturbing soft breakings exist in the literature. We calculate the ratios of string tensions in softly broken N=2 SU(N) gauge theory testing the recently proposed M-theory pred...

We investigate the behavior of softly broken $N=2$ SQCD at non-zero bare theta angle $\theta_0$, using superfield spurions to implement the SUSY breaking. We find a first-order phase transition as $\theta_0$ is varied from zero to $2 \pi$, in agreement with a prediction of `t Hooft. The low-energy theta angle $\theta_{eff}$, which determines the effective charges of dyonic excitations, has a complicated dependence on $\theta_0$ and breaking parameters.

Considered are ${\cal N}=2\, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ equal mass quark flavors. ${\cal N}=2$ 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 theories with both unbroken and spontaneously broken global flavor s...