Effective lagrangian for supersymmetric theories with intermediate breaking scale

We investigate effective lagrangians in supersymmetric models broken spontaneously at an intermediate energy (～ μ ? M_GUT). It is shown to all orders in perturbation theory that the low-energy interactions of light particles are described by an effective lagrangian with explicit but soft supersymmetry breaking of order μ² / M_GUT.     

A lagrangian formulation of the Wess approach to supersymmetric Yang-Mills theories

We obtain a superspace lagrangian density which reproduces the Wess formulation of supersymmetric gauge theories. The present approach, which is a first-order formalism, gives rise to a lagrangian density polynomial in the Yang-Mills and auxiliary superfields and appears to be stable under quantization and renormalization.     

Superconformal anomalies and the effective lagrangian for pure supersymmetric QCD

We discuss the extent to which the superconformal anomalies constrain the effective lagrangian for pure N = 1 Yang-Mills theory. Assuming that the order parameter describing the model is a single chiral superfield (and allowing its derivatives) we find a larger class of possible models than had been previously noted. We give a detailed analysis of a particularly interesting example and find that it leads to the possibility of spontaneous breakdown of supersymmetry. Thus we conclude that the anomaly constraints by themselves are not sufficient to protect supersymmetry. Some unusual features which seem characteristic of such higher derivative theories are noted. A number of related topics, including the question of gluon condensation, are discussed.     

On the effective lagrangian in the supersymmetric N = 1 Yang-Mills theory

It is shown that supersymmetry breaking does not occur in a supersymmetric Yang-Mills theory with an effective lagrangian (EL) constructed of the simplest composite colourless superfields. Our arguments appear also to be valid for the case of still more complicated models of EL.     

Instantons in supersymmetric theories

Instanton effects are considered for a sample of supersymmetric theories, namely, quantum mechanics, gluodynamics, Higgs model. The problem is how to reconcile the apparent lack of the boson-fermion symmetry in the effective instanton induced interactions with supersymmetry of the corresponding lagrangians. It is shown that in the case of quantum mechanics and the Higgs model there is actually no conflict between supersymmetry and the instanton calculus since the Ward identities, associated with the supersymmetry transformations, are satisfied. In quantum mechanics this is due to spontaneous symmetry breaking, or pole terms in matrix elements of supercharge, while in the case of the supersymmetric Higgs model the effective fermion interaction just reduces to a total derivative. In the case of supersymmetric gluodynamics, however, the standard instanton calculus explicitly violates naive Ward identities.     

Decoupling in supersymmetric theories

We examine the decoupling of massive states in supergravity theories. Using superspace functional techniques to “integrate out” the massive modes we derive the effective low-energy lagrangian. The technique is extended to the case of large supersymmetry breaking and we show how the effective lagrangian correctly accounts for vacuum expectation values of massive fields. We discuss the structure of effective theories following from the superstring in which the effects of Kaluza-Klein modes and states massive after intermediate scale breaking are included. It is shown in the case of large intermediate scale breaking the theory should possess discrete symmetries to protect light states from large supersymmetry breaking and we list the conditions for viable models.     

Anomaly cancellations in the local supersymmetric Siegel lagrangian

The local supersymmetric Siegel action for two-dimensional chiral bosons and fermions is studied. It is found that the theory has local supersymmetry anomalies as well as gravitational-like anomalies. A modification of the lagrangian yielding anomaly cancellations is obtained.     

Heavy-particle-induced effective lagrangian in spontaneously broken theories (II). The abelian Higgs-Kibble model

In the context of the abelian Higgs-Kibble model with a charged fermion, we study in detail low-energy effective field theories of light particles when the heavy mass scales in the theory are generated by the Higgs-Kibble mechanism. Our analysis is based on the systematic use of factorization methods, and is valid to all orders in renormalized perturbation theory. Emphasis is given to finding the vestiges of the original (spontaneously broken) local gauge symmetry left in low-energy effective field theories, and general techniques are developed for that purpose. When only Fermi fields or / and physical Higgs fields correspond to light particles, low-energy effective field theories do not exhibit such signs. On the other hand, when physical gauge fields (together with other unphysical fields) correspond to light particles, the original local gauge symmetry restricts the resulting low-energy effective local action to a non-trivial form.     

Dilaton effective lagrangian in gluodynamics

The lagrangian of gluodynamics does not contain dimensional parameters. As a consequence, there emerges an infinite set of Ward identities connecting n-point functions induced by the operator σ = θ_μμ, where θ_μv stands for the regularized energy-momentum tensor. We construct an effective (tree) lagrangian which includes one scalar meson field and saturates automatically all the Ward identities.     

New inflation in supersymmetric theories

A new inflationary universe scenario is considered based upon phase transitions in supersymmetric unified models where the Higgs potential is of the Witten-O'Raifeartaigh type.     

Flavour violation in supersymmetric theories

We investigate in detail the question of lepton-flavour violation in a SU(2) × U(1) supersymmetric model, where the breaking of supersymmetry (SUSY) is achieved through the coupling to N = 1 supergravity. It is shown that in the limit of degenerate neutrino masses, lepton flavour is exactly conserved. Allowing for neutrino masses compatible with present experimental limits, we analyse SUSY contributions to several lepton-flavour violating processes, comparing the size of these contributions with those already present in the standard Glashow-Salam-Weinberg model. In the case of μ → eγ, SUSY leads to a branching ratio two or three orders of magnitude larger than the corresponding branching ratio in the standard model, for gravitino and photino masses compatible with the experimental limits on the muon anomalous magnetic moment. In contrast, SUSY contributions to are always small, of the order of 10⁻² of the corresponding amplitudes in the standard model, if the gravitino and photino masses are constrained by the K_L − K_S mass difference.     

Degenerate representations in supersymmetric theories

Degenerate representations are theoretically constructed with the Neveu-Virasoro algebra. The differential relation is derived from the correlation functions in these representations.     

Instanton effects in supersymmetric theories

We calculate some simplest n-point functions in supersymmetric Yang-Mills theories contributed by instantons. The result is not vanishing and we discuss some implications of this. In particular, the dynamics of the supersymmetric theories must exhibit some unusual features.     

Chiral anomalies in supersymmetric theories

The supersymmetric non-abelian chiral anomaly is computed in a theory of chiral scalar superfields coupled to external gauge superfields, both in a vector-current conserving scheme and in a left-right symmetric scheme. The corresponding supersymmetric Wess-Zumino term is discussed; in particular we give an explicit expression for the anomalous bosonic term.