SPA7031U/P - 2023/24

Enrolment options

SPA7031U/P - Supersymmetric Methods in Theoretical Physics - 2023/24

Here is a rough idea of what will be covered (if you have any comments or are interested in taking the course, please feel free to email me):

Aims and objectives:

The main aim of this course is to introduce fundamental aspects of theoretical physics---symmetries and constraints on the behavior of quantum systems, renormalization, and dualities---through the filter of supersymmetry. In particular, we will tackle various non-trivial examples of these phenomena in a manageable and calculable way. By spending most of the course in three space-time dimensions, we can learn some of the basics of quantum dynamics at strong coupling just using matter superfields and abelian gauge multiplets. This course is designed to be useful for students interested in various theoretical sub-disciplines like particle physics, condensed matter, and string theory.

Syllabus:

Starting with supersymmetric quantum mechanics as a toy model, the course covers the supersymmetry algebra, its representations, the Witten Index, and the resulting constraints on quantum dynamics. We then move on to introduce supersymmetric field theories in three space-time dimensions consisting of scalars and fermions while giving a basic introduction to symmetry currents, the classical and quantum Wilsonian renormalization group flow, moduli spaces, spurions, and non-renormalization arguments. The course is designed to culminate with a study of dualities in three-dimensional supersymmetric abelian gauge theories. However, if time permits, we may also discuss basic aspects of dualities with broken supersymmetry, explicit applications of superspace techniques to condensed matter systems, or embeddings of some of our dualities in string theory.

Pre-requisites:

SPA6413 Quantum Mechanics B, SPA6324 Mathematical Techniques 4 or equivalents

Co-requisites:

SPA7018P Relativistic Waves and Quantum Fields or equivalent