Description

In the search for a unified description of all the forces in Nature, in the 1970s physicists ran into the concept of supersymmetry, a hypothetical symmetry of Nature which relates bosons (particles with integer spin) to fermions (particles with half-integer spin). It was then realised that supersymmetry is the largest symmetry that relativistic quantum field theories of particles can have. Its main consequence is to make the quantum properties of a theory much simpler and more controllable than for ordinary quantum field theories. These features make supersymmetry appealing in constructing models of particle physics, and likely a necessary ingredient to unify quantum physics with gravity.

In the first part of the project, we will discuss how particles can be viewed as irreducible representation of the Poincaré group (combining translations and Lorentz transformations) and how to formulate field theories of bosons and fermions. We will then introduce the supersymmetry algebra and its representations, the so called supermultiplets which package bosons and fermions in a single object. Finally, we will learn how to formulate supersymmetric quantum field theories, using the formalism of superspace and superfields, which generalise Minkowski spacetime and ordinary fields.

In the second part of the project, you may investigate a few uses of these ideas. On the applied side, you may learn how to formulate a supersymmetric version of the Standard Model of particle physics and how to break supersymmetry. On the theoretical side, you may learn how to make exact calculations using supersymmetry, study the links between supersymmetry and geometry, or learn about the uses of supersymmetry in String Theory.

Prerequisites and corequisites

• Mathematical Physics II / Theoretical Physics 2
• Quantum Mechanics III / Foundations of Physics 3A
• Advanced Quantum Theory IV / Theoretical Physics 3 (recommended but not necessary).

References

For some context:

• Wikipedia article on Supersymmetry.

Reading material:

• D. Tong, Lectures on Quantum Field Theory.
• S. Weinberg, The Quantum Theory of Fields.
• A. Bilal, Introduction to Supersymmetry.
• J. Terning, Modern Supersymmetry: Dynamics and Duality.
• P. Argyres, An Introduction to Global Supersymmetry.
• M. Bertolini, Lectures on Supersymmetry.

Advanced reading material on mathematical aspects:

• K. Hori et al., Mirror Symmetry (Part 2).

Note

Since I will be on research leave during Epiphany, supervision is likely to happen over Skype or Zoom in that period.