Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from symmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay π⁰ → γγ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay a → γγ in a supersymmetric composite model might be suppressed with the same mechanism that works for π⁰ → γγ in SQCD.     

Runaway vacuum and supersymmetry

We consider a supersymmetric variant of the vacuum alignment condition. Its consequences in theories with pseudo Goldstone bosons are discussed.     

Quasi nambu-goldstone fermions

We explore in detail the hypothesis that quarks and leptons are the approximately massless quasi Goldstone fermions of a supersymmetric preon theory. In particular, we discuss the possible patterns of states emerging from the spontaneous breakdown of global symmetries in supersymmetric theories and construct the low-energy effective lagrangians describing the interaction of these states. In contrast to what happens in the Goldstone sector, the interactions of the quasi Goldstone fermions contain arbitrary parameters which directly reflect the preon dynamics. Various models are explored, including both models in which the weak interactions are residual and models where these interactions are fundamental. A variety of issues are addressed, from the universality and approximate SU(2)_L nature of the weak interactions, for the former class of models, to the generation of states beyond the quarks and leptons and the nature of the dynamical breaking of SU(2)_L×U(1), for the latter class of models. Open questions and speculations connected with the origin of families and the nature of fermion mass generation, including supersymmetry breaking, are also discussed.     

Weak interactions of quasi nambu-goldstone fermions

We investigate the hypothesis that the observed weak interactions are the residual interactions of quasi Goldstone fermions. Left-handed quarks and leptons arise from the spontaneous symmetry breaking U(6) → U(4) × SU(2) in a supersymmetric theory. The simplest preon model realizing this breakdown leads, in the complementary picture, to the supersymmetric extension of the standard model of electroweak interactions. Furthermore, 't Hooft's anomaly conditions are satisfied with respect to the unbroken subgroup of the U(6) flavour symmetry and R-invariance. The preon model predicts the existence of a ninth chiral supermultiplet, the novino.     

Pseudo-symmetry currents and PCAC in supersymmetric goldstone theories

We present a formalism describing the dynamical properties of Goldstone fields in N = 1 supersymmetric theories. The concept of pseudo-symmetry currents is introduced. This allow us to deal with complex extended pseudo-symmetries of the superpotential in a manner similar with conventional symmetries. Within this framework we generalize the usual PCAC relations.     

Gauge-invariant effective lagrangians for goldstone-like particles of supersymmetric technicolor models

We point out that generally the low-energy spectrum in supersymmetric technicolor models contains quasi-Goldstone fermions and quasi-Goldstone bosons in addition to the usual (pseudo)- Goldstone bosons. Using the language of Kähler geometry, we present a step-by-step procedure for constructing gauge-invariant non-linear lagrangians involving the fermionic and bosonic Goldstone particles in situations in which supersymmetry is preserved. Both the cases of fully gauged and partially gauged global symmetries are considered. We discuss the dynamical version of the super-Higgs mechanism, and we illustrate it with the supersymmetric Susskind-Weinberg technicolor model.     

Partial spontaneous breaking of two-dimensional supersymmetry

We construct low-energy Goldstone superfield actions describing various patterns of the partial spontaneous breakdown of two-dimensional N=(1,1), N=(2,0) and N=(2,2) supersymmetries, with the main focus on the last case. These nonlinear actions admit a representation in the superspace of the unbroken supersymmetry as well as in a superspace of the full supersymmetry. The natural setup for implementing the partial breaking in a self-consistent way is provided by the appropriate central extensions of D=2 supersymmetries, with the central charges generating shift symmetries on the Goldstone superfields. The Goldstone superfield actions can be interpreted as manifestly worldsheet supersymmetric actions in the static gauge of some superstrings and D1-branes in D=3 and D=4 Minkowski spaces. As an essentially new example, we elaborate on the action representing the 1/4 partial breaking pattern N=(2,2)→N=(1,0).     

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.     

A generalized Slavnov-invariant Abelian Higgs-Kibble model

The supersymmetric structure of the Becchi-Rouet-Stora invariance is used for investigating the Abelian Higgs-Kibble model. It allows for a symmetric photon mass M, in which case a massless scalar state corresponding to the Goldstone model belongs to the physical sector. If M = 0, i.e. the photon mass is generated by the Higgs mechanism, this state is decoupled from the physical sector, as usual. The BPHZ renormalization procedure is used.     

A scenario for SUSY QCD

The following scenario is proposed for supersymmetric QCD: With massless (s) quarks, there is a continuum of vacua, including one with all global symmetries unbroken; with (s) quarks of mass m, there is a unique vacuum, no Goldstone bosons, but a rich spectrum of scalars and fermions of mass O(m). Consistency with various non-perturbative requirements is exhibited.     

Nonhermitian supersymmetric partition functions: The case of one bosonic flavor

We discuss the supersymmetric formulation of the nonhermitian β=2$\beta =2$ random matrix partition function with one bosonic flavor. This partition function is regularized by adding one conjugate boson and fermion each. A supersymmetric nonlinear σ-model for the resulting Goldstone degrees of freedom is obtained using symmetry arguments only. For a Gaussian probability distribution the same results are derived using superbosonization and the complex orthogonal polynomial method. The symmetry arguments apply to any model with the same symmetries and a mass gap, and demonstrate the universality of the nonlinear σ-model.     

Nonperturbative nonrenormalization theorem for supersymmetric QCD

We show that no radiative masses are acquired by the Goldstone pion supermultiplet in supersymmetric QCD. Thus, in contrast to ordinary QCD, the mass difference m_π²+−m_π²0 remains zero even after electromagnetism is turned on. Bound state Goldstone supermultiplets obey a nonrenormalization theorem analogous to that obeyed by elementary chiral superfields.     

Internal symmetry currents and supersymmetric effective lagrangians

A supersymmetric and non-linearly realized internally symmetric action is constructed from the super Kähler potential of Goldstone scalar superfields. Noether's theorem in superspace is derived and the associated superfield of currents defined. The currents are used to derive a super Dashen formula relating the (quasi) Goldstone masses and decay constants to the symmetry breaking part of the theory and to supersymmetrically gauge the invariant subgroup as well as the full group.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Mixing between gravitational and weak interactions through the massive gravitino

The interactions of the Goldstone neutrino, in a globally supersymmetric theory, are shown to depend only on the mass spectrum. If supersymmetry is realized locally, the Goldstone neutrino is eliminated by the super-Higgs mechanism; the gravitino (spin $\text{3}\text{2}$ partner of the gravition) becomes massive, leading to a mixing between gravitational and weak interactions. Weak interactions of the gravitino, for example weak decays of heavy new particles, can be recovered as a special case of gravitational ones.     

Temperature and supersymmetry

We study equal-time correlation functions at finite temperature in field theories with global supersymmetry. Global supersymmetry is found to be broken at finite temperature; the ground state is not supersymmetric but no Goldstone fermion appears. The temperature dependence of the mass spectrum in the one-loop approximation and leading order in temperature is investigated in several models. In the models that we consider with spontaneous supersymmetry breaking we find that the Goldstone fermion remains massless at the one-loop level. Ward identities describing the supersymmetry of the underlying theory are checked at the one-loop level. We also discuss the situation in supergravity.     

Chiral quarks and proton decay

In this paper we calculate the hadronic matrix elements of baryon decay operators using a chiral effective lagrangian with quarks, gluons and Goldstone boson fields. We study in detail the cases where the ΔB = 1 operators arise from supersymmetric SU(5) GUT as well as the minimal SU(5) GUT model. In each model the results depend on two parameters. In particular there is a range of values for the two parameters, where the dominant decay modes in the minimal SU(5) GUT are: p → ηe⁺ and n → π^? e⁺.     

Chiral symmetry breaking in SQCD

Using a spectral function sum rules approach, we derive some constraints among the Goldstone parameters, the lowest dimension vacuum condensates and the mass of the chiral matter superfield in supersymmetric QCD (SQCD). These relations are consistent with previous results on SQCD and complement them.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.