``Integrating in'' and exact superpotentials in 4d

We discuss integrating out matter fields and integrating in matter fields in four dimensional supersymmetric gauge theories. Highly nontrivial exact superpotentials can be easily obtained by starting from a known theory and integrating in matter.Comment: 10 pages, RU-94-5

Mixed quark-gluon condensate from instantons

We calculate the vacuum expectation value of the dimension-5 "mixed" quark-gluon operator, $O_\sigma = \bar\psi (\lambda^a /2) \sigma_{\mu\nu} \psi F_{\mu\nu}^a$, in the instanton vacuum. Within the $1/N_c$--expansion the QCD operator is replaced by an effective many-fermion operator, which is averaged over the effective theory of massive quarks derived from instantons. We find $m_0^2 \equiv \langle O_\sigma \rangle / \langle \bar\psi\psi \rangle \approx 4 \bar\rho^{-2} = 1.4 GeV^2$, somewhat larger than the estimate from QCD sum rules for the nucleon.Comment: 10 p, LaTeX, 1 figure included using eps

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

A Chiral SU(N) Gauge Theory Planar Equivalent to Super-Yang-Mills

We consider the dynamics of a strongly coupled SU(N) chiral gauge theory. By using its large-N equivalence with N=1 super-Yang-Mills theory we find the vacuum structure of the former. We also consider its finite-N dynamics.Comment: 10 pages, Latex. 1 eps figur