The Conformal Bootstrap in higher dimensions(d>2)

Ghosh, Soham (2021) The Conformal Bootstrap in higher dimensions(d>2). Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Soham Ghosh (16MS035)) 16MS035_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (656kB)

Abstract

In the regime of non perturbative studies of Quantum Field Theories the Conformal Bootstrap Programme is a very exciting research direction. One of the biggest goals of this programme is to provide a totally non-perturbative formulation of conformally invariant Quantum Field Theories, eliminating the need for a Lagrangian description. This research approach relies on solving and/or constraining a Conformally invariant Quantum Field Theory by means of its own self consistency, thus paving the way for a redefinition of Conformal Field Theories(CFTs). It is quite remarkable that solely using arguments following from locality, unitarity and symmetry we can derive the bootstrap consistency conditions. My project work relies on describing the foundations of such an approach that I have learned by meticulously studying the TASI lecture notes of David Simmons-Duffin[12] and EPFL lecture notes of Slava Rychkov [11], explicitly solving all the insightful exercises suggested there. Finally, at the end I have worked out two examples that shows the power of The Conformal Bootstrap, in describing beautiful aspects of CFTs.

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