Arthur Hebecker - Naturalness, String Landscape and Multiverse: A Modern Introduction with Exercises

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This course intends to give a concise but technical introduction to Physics Beyond the Standard Model and early cosmology as seen from the perspective of string theory. Basics of string theory will be taught as part of the course. As a central physics theme, the two hierarchy problems (of the cosmological constant and of the electroweak scale) will be discussed in view of ideas like supersymmetry, string theory landscape, eternal inflation and multiverse. The presentation will include critical points of view and alternative ideas and explanations. Problems with solutions are also provided to facilitate the use of these notes in classroom and for self-study.

Basic knowledge of quantum field theory (QFT), general relativity and cosmology will be assumed. Supersymmetry, elements of supergravity and fundamentals of string theory will be taught together with a number of geometrical concepts needed to study string compactifications. However, given the limited scope of a one-semester lecture series, this can clearly not replace a full string theory course or the detailed study of string geometry.

The author has taught this course at Heidelberg University with the intention to prepare students who have taken a two-semester QFT and a one-semester relativity course for masters thesis research in string phenomenology. Another goal was to allow students who intend to do research in particle phenomenology, cosmology or formal (mathematical) string theory to develop some basic understanding of the possible relation of string theory to real-world physics and its most fundamental problems.

For students who had the privilege of enjoying a complete graduate-level education (with full lecture courses on strings and supersymmetry/supergravity) before embarking on research, most of the material in the first part of this course will be familiar. Still, depending on the focus of their string and cosmology courses, they may find useful additional information about landscape, multiverse, eternal inflation and alternative perspectives in the second half of the course.

The detailed plan of the lecture notes is as follows: We will start in Chap. , we end by summarising the overall picture and the challenges that should have crystallised during the study of this course.

While useful references for background material and deeper exploration will be provided as we go along, it may not hurt to give some essential literature right away: Good sources for the background knowledge in QFT and relativity are [1] and [2], respectively. For more details on Standard Model and particle-physics-related topics, Refs. [3, 4] represent useful sources. For supersymmetry and supergravity, see [5, 6]. Two of the most complete modern string theory textbooks are [7, 8]. Concerning string phenomenology, [9] represents a very comprehensive monograph, which, in particular, covers the important subjects of how specific gauge and matter sectors are realised in string compactificationsa topic that we treat very superficially in this course. A very useful set of notes emphasising the geometric side of how the landscape arises from string theory is [10]. For a detailed review of string landscape physics, see [11].