Edward Shuryak - Nonperturbative Topological Phenomena in QCD and Related Theories

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The book is a summary of various lectures on nonperturbative QCD which I have given during the last three decades at Stony Brook. It is about the topological objects present in gauge theories, their semiclassical theory, and applications to multiple physical phenomena. The overall content of the book can be grasped from the list of chapters and sections below, so let me mention here, at the start, what is different in this book relative to others. There are good classic reviews, books, and lecture notes on magnetic monopoles and instantons. Yet those about instanton-dyons, sphalerons, and even such traditional object as QCD flux tubes are yet to be found. Even for subjects on which there is extensive pedagogic-style literature, they all have rather different focus. Usually these objectstopological solitons, as one can call them collectivelyare treated individually. (It can be compared to a visit to a zoo: here is a lion, and here is a gazelle, etc.)

Of course, we will have similar individual discussion of all these objects below as well, but the focus will be on their ensembles and phenomena which such objects generate collectively. (Think of it as an actual trip to African savannas.) For example, at some settings, such solitons can exist in finite cluster or groups and in another in infinite (scaled as volume) condensates. Under certain conditions, monopoles undergo Bose-Einstein condensation, related to confinement-deconfinement phase transitions. Instantons lead to quark pairing and condensation, breaking spontaneously the chiral symmetry. This leads to effective quark mass (and therefore large fraction of the nucleons massas well as our own!). Sphalerons lead to chiral imbalance in heavy ion collisions and in early Universe, producing also sounds, gravity waves, and perhaps even the baryon asymmetry.

The semiclassical models of all these phenomena have also strong roots in the first-principle numerical approach to gauge theories, known as lattice gauge theories. For all of these objects, observations of them on the lattice, and verification of their collective effects, would also be the important part of many chapters below.

Crucial feature of modern field/string theories is a notion of dualities, namely, existence of different yet physically equivalent descriptions. We will discuss three of those: (1) the famed electric-magnetic duality; (2) the Poisson duality, e.g., between monopoles and instanton-dyons; as well as (3) the holographic gauge-string or AdS/CFT duality. Discovery of each duality is always a surprise, complemented with original disbelief, then some confusion, and finally multiple tests. This makes internal logic of a book a bit complex, since some chapters are dual to others. Let me illustrate the situation for Poisson duality, much less known than the others. It tells us that the partition function (and of course everything else, stemming from it) using