Supersymmetric field theories by Sergio Cecotti

Abstract

<p>Supersymmetry is a subject that is vast, beautiful and yet often poorly described in textbooks. Notation is a crucial barrier difficult for authors to successfully hurdle – the beautiful and deep concepts of supersymmetry are nestled deep, hidden behind a slew of formalism that can be hard to grasp even for experienced researchers. At the same time, authors must be precise: a description of ideas without equations is not very useful at a practical level for students and researchers alike. The challenge then is to strike balance between conveying the concepts as well as calculation tools to make them useful. Cecotti in his new book ‘Supersymmetric Field Theories’ does this well. Mathematically powerful, but also clearly written in language accessible to graduate students, he describes some of the most recent advances in supersymmetry and related subjects. In fact, he covers a vast range of subjects: from the special geometry of moduli spaces to dualities of supersymmetric quantum field theories. The theme of topics covered is largely centred on geometric structures and dualities and these are where some of the most beautiful ideas lie. The book assumes a working knowledge of basic supersymmetry, and is not only intended for advanced graduate students, but is also an excellent reference for active researchers. The book is structured into three broad parts. Part I introduces how geometric structures emerge from supersymmetric field theories, such as G-structure and special Kahler geometry. Many of these geometric structures become enhanced when the amount of supersymmetry is increased beyond eight supercharges, and this is the subject of Part II. Symmetries such as U-duality of the moduli spaces of space–time supersymmetric and supergravity theories are nicely described, as well as more obscure topics such as Grassmannians. An important aspect of flux compactification of string theories is the Killing spinor analysis of supergravity theories, and this is also covered in Part II. Finally, theories with more than eight supercharges are also covered, including the ABJM model of M2-branes. Finally, Part III is a discussion of special geometry, including a variety of classic topics such as Kodaira–Spencer theory and the special geometry of N = 2 supergravity theories. Although mathematically phrased, Cecotti never strays far from the physics of these theories, and is self-contained including a description of any mathematical terminology. Altogether, a valuable resource for students and academics alike.</p>