On {\cal N}=1 exact superpotentials from U(N) matrix models

In this letter we compute the exact effective superpotential of {\cal N}=1 U(N) supersymmetric gauge theories with N_f fundamental flavors and an arbitrary tree-level polynomial superpotential for the adjoint Higgs field. We use the matrix model approach in the maximally confinig phase. When restricted to the case of a tree-level even polynomial superpotential, our computation reproduces the known result of the SU(N) theory.Comment: 15 pages, LaTe

Transfinite reductions in orthogonal term rewriting systems

Strongly convergent reduction is the fundamental notion of reduction in infinitary orthogonal term rewriting systems (OTRSs). For these we prove the Transfinite Parallel Moves Lemma and the Compressing Lemma. Strongness is necessary as shown by counterexamples. Normal forms, which we allow to be infinite, are unique, in contrast to ω-normal forms. Strongly converging fair reductions result in normal forms. In general OTRSs the infinite Church-Rosser Property fails for strongly converging reductions. However for Böhm reduction (as in Lambda Calculus, subterms without head normal forms may be replaced by ⊥) the infinite Church-Rosser property does hold. The infinite Church-Rosser Property for non-unifiable OTRSs follows. The top-terminating OTRSs of Dershowitz c.s. are examples of non-unifiable OTRSs

Infinitary lambda calculus

In a previous paper we have established the theory of transfinite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of infinitary rewriting, the Böhm model of the lambda calculus can be seen as an infinitary term model. In contrast to term rewriting, there are several different possible notions of infinite term, which give rise to different Böhm-like models, which embody different notions of lazy or eager computation