Instantons And Large N

A highly pedagogical textbook for graduate students, exploring advanced topics of quantum field theory with detailed derivations and worked examples.

The generalization of QCD from three to N C colors, developed in 1974 by Nobel laureate Gerard ''t Hooft, has proved to be an extraordinarily useful and robust theoretical extension for studying the behavior of strong interaction physics. This book is the proceedings of the first-ever meeting exclusively devoted to large N C QCD. The workshop brought together representatives of many subdisciplines for a OC meeting of mindsOCO on topics ranging from finite temperature and density to the lattice, perturbative QCD, instantons, mesons, baryons, and nuclear physics. Beginning with ''t Hooft''s keynote presentation, the contributions are designed to introduce uses of large N C methods in each specialty to a broader particle physics audience."

Opening lectures. Sid Coleman and Erice / A. Zichichi. Remembering Sidney Coleman / G.'t Hooft -- Predicted signals at LHC. From extra-dimensions : Multiple branes scenarios and their contenders / I. Antoniadis. Predicted signals at the LHC from technicolor / A. Martin. The one-parameter model at LHC / J. Maxin, E. Mayes and D.V. Nanopoulos. How supercritical string cosmology affects LHC / D.V. Nanopoulos. High scale physics connection to LHC data / P. Nath. Predicted signatures at the LHC from U(I) extensions of the standard model / P. Nath -- Hot theoretical topics. Progress on the ultraviolet finiteness of supergravity / Z. Bern. Status of supersymmetry : Foundations and applications / S. Ferrara and A. Marrani. Quantum gravity from dynamical triangulation / R. Loll. Status of superstring and M-theory / J.H. Schwarz. Some effects of instantons in QCD / G.'t Hooft. Crystalline gravity / G.'t Hooft -- QCD problems. Strongly coupled gauge theories / R. Kenway. Strongly interacting matter at high energy density / L. McLerran. Seminars on specialized topics. The nature and the mass of neutrinos. Majorana vs. Dirac / A. Bettini. The anomalous spin distributions in the nucleon / A. Deshpande. Results from PHENIX at RHIC / M.J. Tannenbaum -- Highlights from laboratories. Highlights from RHIC / Y. Akiba. News from the Gran Sasso Underground Laboratory / E. Coccia. Highlights from TRIUMF / N.S. Lockyer. Highlights from Superkamiokande / M. Koshiba. Highlights from Fermilab / P.J. Oddone. Highlights from IHEP / Y. Wang -- Special sessions for new talents. Fake supergravity and black hole evolution / A. Gnecchi. Track-based improvement in the jet transverse momentum resolution for ATLAS / Z. Marshall. Searches for supersymmetric dark matter with XENON / K. Ni. Running of Newton's constant and quantum gravitational effects / D. Reeb

This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.

Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

In August/September 2002, a group of 78 physicists from 50 laboratories in 17 countries met in Erice, Italy, to participate in the 40th Course of the International School of Subnuclear Physics. The purpose of the School was to focus attention on the theoretical and phenomenological developments in gauge theories, as well as in all the other sectors of subnuclear physics. Experimental highights from the most relevant sources of new data were presented and discussed, including the latest news on theoretical developments in quantizing the gravitational forces. This volume constitutes the proceedings of the School. It is dedicated to the memory of Victor Frederick Weisskopf, a founder OCo together with John Stewart Bell, Patrick Maynard Stuart Blackett and Isidor Isaac Rabi OCo of the OC Ettore MajoranaOCO Centre for Scientific Culture, this School being the first of its 114 Schools now in existence. Contents: Mini-Courses on Basics: Physics of QCD Instantons (E V Shuryak); Confinement and Duality (M J Strassler); Status of Super String Theory (E Verlinde); Perturbative Quantum Gravity (G ''t Hooft); Experimental Highlights: Highlights from Gran Sasso Laboratory (A Bettini); Experimental Highlights from Super-Kamiokande (Y Totsuka); The Fermilab Experimental Physics Program (R Tschirhardt); Special Sessions for New Talents: Application of the Large- N c Limit to a Chiral Lagrangian with Resonances (O Cata); Towards the Finite Temperature Gluon Propagator in Landau Gauge YangOCoMills Theory (A Maas); Hermes Measurements of the Nucleon Spin Structure (J Wendland); and other papers. Readership: High energy, experimental and theoretical physicists."

This volume is a compilation of works which, taken together, give a complete and consistent presentation of instanton calculus in non-Abelian gauge theories, as it exists now. Some of the papers reproduced are instanton classics. Among other things, they show from a historical perspective how the instanton solution has been found, the motivation behind it and how the physical meaning of instantons has been revealed. Other papers are devoted to different aspects of instanton formalism including instantons in supersymmetric gauge theories. A few unsolved problems associated with instantons are described in great detail. The papers are organized into several sections that are linked both logically and historically, accompanied by extensive comments.