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, which can be in the same quantum state) to fermions (particles with half-integer spin, which cannot be in the same quantum state). It was soon realised that supersymmetry is the largest spacetime symmetry that relativistic quantum field theories of particles can have, if the theory depends on the energy scale at which it is probed. Another key consequence of supersymmetry is to allow stronger theoretical control on the quantum properties of the theory. 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 (mathematically, a representation). 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 study how to break supersymmetry and make connection with the real world. On the theoretical side, you may learn how to make exact calculations using supersymmetry, study the links between supersymmetry and geometry, or learn about some of the uses of supersymmetry in String Theory.

Prerequisites and corequisites

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