Points, Lines, and Surfaces at Criticality

Description

This thesis offers a fascinating journey through various non-perturbative aspects of Conformal Theories, in particular focusing on the Conformal Bootstrap Programme and its extensions to theories with various degrees of symmetry. Because of the preeminent role of Conformal Theories in Nature, as well as the great generality of the results here obtained, this analysis directly applies to many different areas of research. The content of this thesis is certainly relevant for the physics community as a whole and this relevance is well motivated and discussed along the various chapters of this work. The work is self-contained and starts with an original introduction to conformal theories, defects in such theories and how they lead to constraints on data and an extension of the bootstrap programme. This situation is often realized by critical systems with impurities, topological insulators, or – in the high-energy context – by Wilson and 't Hooft operators. The thesis continues with original research results of the author, including supersymmetric extensions. These results may be relevant non only in the high energy physics context - where supersymmetry is required for the theory to be consistent - but also for condensed matter systems that enjoy supersymmetry emergence at long distances. Front Matter ....Pages i-xiii Preamble (Edoardo Lauria)....Pages 1-5 Introduction to Conformal Field Theories (Edoardo Lauria)....Pages 7-39 Defects in Conformal Field Theories (Edoardo Lauria)....Pages 41-90 An Étude on \(\mathcal {N}=2\) Conformal Manifolds in 3d (Edoardo Lauria)....Pages 91-136 Superconformal Blocks for SCFTs with Eight Supercharges (Edoardo Lauria)....Pages 137-157 Conclusion (Edoardo Lauria)....Pages 159-161 Back Matter ....Pages 163-164