We construct a manifestly gauge invariant Lagrangian in 3 + 1 dimensions for N Kaluza-Klein modes of an SU(m) gauge theory in the bulk. For example, if the bulk is 4 + 1, the effective theory is Π N +1 i=1 SU(m) i with N chiral (m, m) fields connecting the groups sequentially. This can be viewed as a Wilson action for a transverse lattice in x 5 , and is shown explicitly to match the continuum 4+1 compactified Lagrangian truncated in momentum space. Scale dependence of the gauge couplings is described by the standard renormalization group technique with threshold matching, leading to effective power law running. We also discuss the unitarity constraints, and chiral fermions. *

We consider Flavour Changing Neutral Current processes in the framework of the supersymmetric extension of the Standard Model. FCNC constraints on the structure of sfermion mass matrices are reviewed. Furthermore, we analyze supersymmetric contributions to FCNC transitions which remain in the limit of flavourconserving sfermion mass matrices. Implications of the FCNC constraints on the structure of sfermion mass matrices for SUSY breaking and sfermion mass generation are discussed. We conclude that the supersymmetric flavour problem is intriguing but perhaps not as severe as it is commonly believed.

Quantum field theory forms the present theoretical framework for our understanding of the fundamental interactions of particle physics. This up-dated and expanded text examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. Beginning with a new chapter giving a systematic introduction to classical field theories and a short discussion of their canonical quantization and the discrete symmetries C, P and T, the book provides a brief exposition of perturbation theory, the renormalization programme, and the use of the renormalization group equation. It then explores topics of current research interest including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry. A chapter on basics of the electroweak theory is now included. Professor Pokorski, a distinguished theoretical physicist, has presented here a self-contained text for graduate courses in physics; the only prerequisite is some grounding in quantum field theory.

We discuss the reduction of the eleven-dimensional M-theory effective Lagrangian, considering first compactification from eleven to five dimensions on a Calabi-Yau manifold, followed by reduction to four dimensions on an S 1 /Z 2 line segment at a larger distance scale. The CalabiYau geometry leads to a structure of the five-dimensional Lagrangian that has more freedom than the eleven-dimensional theory. In five dimensions one obtains a non-linear σ model coupled to gravity, which implies non-trivial dynamics for the scalar moduli fields in the bulk of the Z 2 orbifold. We discuss solutions to the five-dimensional equations of motion in the presence of sources localized on the boundaries of the Z 2 orbifold that may trigger supersymmetry breaking, e.g., gaugino condensates. The transmission of supersymmetry breaking from the hidden wall to the visible wall is demonstrated in specific models. The rôle of the messenger of supersymmetry breaking may be played by the gravity supermultiplet and/or by scalar hypermultiplets. The latter include the universal hypermultiplet associated with the Calabi-Yau volume, and also the hypermultiplets associated with deformations of its complex structure, which mix in general.