Date of Award

May 2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor(s)

Simon M. Catterall

Keywords

Gauge theories, Holography, Matrix models, Quantum gravity, Supersymmetry

Subject Categories

Physical Sciences and Mathematics

Abstract

Lattice studies of strongly coupled gauge theories started with the pioneering work of Wilson. The success of lattice QCD since then has improved our understanding of strong dynamics, crucial for a proper understanding of many interesting phenomena in Physics. However, it is now known that the Standard model is only an approximation to some richer underlying theory. It is believed that supersymmetry has a special role to play in the framework of that theory. Even if nature is non-supersymmetric at all energy scales and we see no experimental evidence for it in the coming decades, the beautiful structure of these theories could still be very important in our quest to understand the universe. In four dimensions, a special supersymmetric theory has drastically altered our understanding of the holographic principle. In view of these observations, the study of supersymmetric gauge theories on the lattice at strong couplings is crucial. Even though lattice supersymmetry has a long history going back four decades, it has been very difficult to simulate the four-dimensional theory at strong couplings until now. This is because supersymmetry on the lattice is far from trivial and is broken at the clas- sical level because of the supersymmetric algebra. However, substantial progress has been made in studying these theories on the lattice. Several wonderful ideas like topological twisting, differential forms, point group symmetries of the lattice, and integer form fermions all come together and has enabled us to study these supersymmetric theories by preserving a subset of supersymmetries exactly on the lattice. This thesis deals with the numerical studies of super Yang-Mills (SYM) theories in various dimensions, their large N limit, and their role in a better understanding of gauge/gravity duality.

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