This introductory chapter first sets out the book's purpose, which is to provide a rigorous proof of the Deser–Schwimmer conjecture. This work is a continuation of the previous two papers of the author, which established the conjecture in a special case and introduced tools that laid the groundwork for the resolution of the full conjecture. The chapter then provides a formulation of the conjecture, presents some applications, and discusses its close relation with certain questions in index theory and in Cauchy–Riemann and Kähler geometry. Then, it broadly outlines the strategy of the proof and very briefly present the tasks that are undertaken in each of the subsequent chapters.
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