Quantum Tunneling

This article is a slightly expanded version of the talk I delivered at the Special Plenary Session of the 46-th Annual Meeting of the Israel Physical Society (Technion, Haifa, May 11, 2000) dedicated to Misha Marinov. In the first part I briefly discuss quantum tunneling, a topic which Misha cherished and to which he was repeatedly returning through his career. My task was to show that Misha's work had been deeply woven in the fabric of today's theory. The second part is an attempt to highlight one of many facets of Misha's human portrait. In the 1980's, being a refusenik in Moscow, he volunteered to teach physics under unusual circumstances. I present recollections of people who were involved in this activity.Comment: Dedicated to the memory of Professor Michael Marinov, a friend, a colleague and a man of firm principles who believed in his right to live in peace in Israel, the land of his ancestors (Latex, 5 eps figures, uses sprocl style), to be published in the Michael Marinov Memorial Volume, Eds. M. Olshanetsky and A. Vainshtein (World Scientific, 2002

Non-Perturbative Yang-Mills from Supersymmetry and Strings, Or, in the Jungles of Strong Coupling

I summarize some recent developments in the issue of planar equivalence between supersymmetric Yang-Mills theory and its orbifold/orientifold daughters. This talk is based on works carried out in collaboration with Adi Armoni, Sasha Gorsky and Gabriele Veneziano.Comment: Based on talks delivered at Planck-05/Mohapatra-Fest, ICTP, Trieste, May 23-28, 2005, and PASCOS-05, Gyeongju, Korea, May 30 - June 4, and the Cracow School of Theoretical Physics, Zakopane, Poland, June 3-12, 2005. 24 pages, 6 figure

Persistent Challenges of Quantum Chromodynamics

Unlike some models whose relevance to Nature is still a big question mark, Quantum Chromodynamics will stay with us forever. Quantum Chromodynamics (QCD), born in 1973, is a very rich theory supposed to describe the widest range of strong interaction phenomena: from nuclear physics to Regge behavior at large E, from color confinement to quark-gluon matter at high densities/temperatures (neutron stars); the vast horizons of the hadronic world: chiral dynamics, glueballs, exotics, light and heavy quarkonia and mixtures thereof, exclusive and inclusive phenomena, interplay between strong forces and weak interactions, etc. Efforts aimed at solving the underlying theory, QCD, continue. In a remarkable entanglement, theoretical constructions of the 1970s and 1990s combine with today's ideas based on holographic description and strong-weak coupling duality, to provide new insights and a deeper understanding.Comment: Julius Edgar Lilienfeld Prize Lecture at the April Meeting of APS, Dallas, TX, April 22-25, 2006; v.2: reference added; v.3: reference adde

Little Miracles of Supersymmetric Evolution of Gauge Couplings

The invention of supersymmetry, almost exactly 25 years ago, changed the face of high-energy physics. The idea that the observed low-energy gauge groups appear due to the process of spontaneous breaking of a single unifying group $G$ is also quite popular. The synthesis of these two elements results in supersymmetric grand unification. I present (perturbatively) exact results regarding the supersymmetric evolution of the gauge couplings from the scale of their unification to lower scales. In particular, it is shown how the heavy mass thresholds can be properly taken into account to all orders.Comment: Extended version of the talk at the 4th International Workshop on Supersymmetry and Unification of Fundamental Interactions -- SUSY-96, May 29 -- June 1, University of Maryland, College Park, MD 20742, USA; 25 pages, 2 figure

Remarks on Adjoint QCD with k Flavors, k>= 2

I summarize what we know of adjoint QCD. Some observations (albeit very simple) are new.Comment: 12 p. 3 figs; v2: a comment and 2 references adde

Quark-Hadron Duality

I review the notion of the quark-hadron duality from the modern perspective. Both, the theoretical foundation and practical applications are discussed. The proper theoretical framework in which the problem can be formulated and treated is Wilson's operator product expansion (OPE). Two models developed for the description of duality violations are considered in some detail: one is instanton-based, another resonance-based. The mechanisms they represent are complementary. Although both models are rather primitive (their largest virtue is their simplicity) they hopefully capture important features of the phenomenon. Being open for improvements, they can be used "as is" for orientation in the studies of duality violations in the processes of practical interest.Comment: Based on the talks delivered at the VIII-th International Symposium on Heavy Flavor Physics, Southampton, UK, 25-29 July 1999, and the International Workshop "Gribov-70", Orsay, France, 27-29 March 2000. To be published in the Boris Ioffe Festschrift "At the Frontier of Particle Physics/Handbook of QCD", Ed. M. Shifman (World Scientific, Singapore, 2001); 41 pages, 14 eps figures, Late