Dynamical breaking of supersymmetry

General conditions for dynamical supersymmetry breaking are discussed. Very small effects that would usually be ignored, such as instantons of a grand unified theory, might break supersymmetry at a low energy scale. Examples are given (in 0 + 1 and 2 + 1 dimensions) in which dynamical supersymmetry breaking occurs. Difficulties that confront such a program in four dimensions are described.     

Dynamical supersymmetry breaking in supersymmetric QCD

The massless limit of supersymmetric QCD with $\text{N}{}_{\mathrm{?}}$ flavors and N colors is analyzed in detail. For $\text{N}{}_{\mathrm{?}}\text{< N}$ there is a unique superpotential which might be generated by non-perturbative effects. We show that it indeed appears, thus violating the non-renormalization theorems. For $\text{N}{}_{\mathrm{?}}\text{= N ? 1}$ instantons produce the superpotential. For $\text{N}{}_{\mathrm{?}}\text{< N ? 1}$ it is again generated, provided that a mild assumption about the dynamics of pure supersymmetric gauge theories is correct. For $\text{N}{}_{\mathrm{?}}\text{? N}$ no invariant superpotential exists; the classical vacuum degeneracy is a property of the full quantum theory. When a small quark mass term is added to the theory $\text{(}\text{for}\text{N}{}_{\mathrm{?}}\text{< N), N}$ supersymmetric ground states, identified with those found by Witten exist. As m → 0 these N vacua wander to infinity, leaving the massless theory without a ground state.     

Softly broken supersymmetry and radiative gauge symmetry breaking

We compare two approaches to quantum corrections in theories with softly broken supersymmetry: the effective potential à la Coleman-Weinberg and the scaling of parameters of the tree level potential between M_PL and M_W, which has been used recently in the context of low-energy supergravity in order to obtain radiative SU(2) × U(1) symmetry breaking. Corrections to the latter procedure are studied in simple models and estimated in the general case.     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

Dynamical supersymmetry breaking in a finite field theoretical model

We present a supersymmetric field theory in two or three space-time dimensions with an internal symmetry of the O(N) type. In the large-N limit the model is finite and supersymmetry is spontaneously broken. The fields representing the order parameters of the broken supersymmetry phase acquire dynamics through quantum corrections. In particular the Goldstone fermion is a zero-mass fermionic bound state.     

Dynamical breaking of supersymmetry and positivity of vacuum energy density

The possibility of dynamical breaking of supersymmetry is investigated with special emphasis on the role of the positivity of the vacuum energy density. We point out that (i) the vacuum energy density can become negative after appropriate renormalization of the fields (thereby being energetically favorable over the supersymmetric case), yet (ii) in such a situation the Nambu-Goldstone fermion state must necessarily possess negative norm, the theory becoming physically unacceptable. This phenomenon is explicitly demonstrated using an O(N) symmetric Wess-Zumino type model in the large-N limit. We conclude that for dynamical breaking of supersymmetry to occur in a physically acceptable manner, it is necessary that supersymmetric solution(s) be completely destroyed. Our study suggests that a strong power-type infrared singularity might achieve such a situation.     

Dynamical symmetry breaking of extended gauge symmetries

We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right gauge group G(LR)=SU(3)(c) x SU(2)(L) x SU(2)(R) x U(1)(B-L), and its extension to the Pati-Salam gauge group G(422)=SU(4)(PS) x SU(2)(L) x SU(2)(R). The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of G(LR) and G422 and the generation of fermion masses. They include a seesaw mechanism for neutrino masses, without a grand unified theory (GUT) scale. These models explain why G(LR) and G422 break to SU(3)(c) x SU(2)(L) x U(1)(Y), and why this takes place at a scale (approximately 10(3) TeV) large compared to the electroweak scale, but much smaller than a GUT scale.     

On the absence of supersymmetry anomalies in gauge theories

It is shown that N = 2 non-abelian gauge theory can be renormalized consistent with gauge invariance, supersymmetry and unitarity. There is no perturbative supersymmetry anomaly: the proof is independent of any specific regulator.     

Electroweak breaking and supersymmetry breaking

We discuss the clash between the absence of fine tuning in the Higgs potential and a sufficient suppression of flavour changing neutral current transitions in supersymmetric extensions of the standard model. It is pointed out that horizontalU(1) symmetry combined with theD-term supersymmetry breaking provides a realistic framework for solving both problems.     

Z'-mediated supersymmetry breaking

We consider a class of models in which supersymmetry breaking is communicated dominantly via a U1' gauge interaction, which also helps solve the mu problem. Such models can emerge naturally in top-down constructions and are a version of split supersymmetry. The spectrum contains heavy sfermions, Higgsinos, exotics, and Z' approximately 10-100 TeV, light gauginos approximately 100-1000 GeV, a light Higgs boson approximately 140 GeV, and a light singlino. A specific set of U1' charges and exotics is analyzed, and we present five benchmark models. The implications for the gluino lifetime, cold dark matter, and the gravitino and neutrino masses are discussed.     

Dynamical supersymmetry breaking in two-dimensional N = 1 supergravity theories

We investigate a possible dynamical mechanism for spontaneous supersymmetrybreaking in N = 1 supergravity theories in 1 + 1 space-time dimensions. It will be shown that supersymmetry is never broken at the tree level, but it can be broken for a certain class of models by quantum effects due to trace anomalies of the energy-momentum tensor and the supercurrent.     

Mixing-induced spontaneous supersymmetry breaking

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two chiral N=1 supermultiplets and arguments for its general validity are given. That is an instance of the O?Raifeartaigh Lagrangian for which there is no tree-level nor perturbative breaking. Nonetheless, the dynamical breaking occurs due to the vacuum condensate, a mixing-induced nonperturbative effect that lifts the zero point energy.     

Constraints on supersymmetry breaking

Some non-perturbative constraints on supersymmetry breaking are derived. It is demonstrated that dynamical supersymmetry breaking does not occur in certain interesting classes of theories.     

Extended supersymmetry and gauge theories

A formulation of gauge theories with an extended supersymmetry for N = 2 is given in terms of superfields. The Lagrangian is expressed in terms of superfields and component fields as well.