Description

Supersymmetric field theories are a particular class of quantum field theories that enjoy a surprising form of symmetry known as supersymmetry, which relates bosonic fields (like the force carriers, such as photons) to fermionic fields (which provide the basic matter particles in Nature, such as electrons and quarks).

The presence of supersymmetry in a theory makes it easier to study. One of the surprises that arose from the study of supersymmetric theories in the 80s and 90s is that they often enjoy the phenomenon of duality: a single quantum field theory admits two (or more) very different semi-classical approximations. Very often, there are interesting questions that are very hard to answer in one classical description that become easier to solve in the dual description. As it turns out, duality is pervasive in supersymmetric quantum field theory and in string theory.

In this project you will answer some of the following questions:

• What is duality?
• More generall, are there cases of \(n\)-ality with \(n>2\)? That is, are there quantum theories with \(n>2\) different classical limits?
• What about $n=0$? That is, are there quantum theories with no classical Lagrangian description? How do we even define these theories?
• How do you test duality?
• In the 80s string theorists discovered 5 different versions of supersymmetric field theory in ten dimensions. In the 90s, it was understood that they are all likely to be secretly the same theory, a mysterious (and still poorly understood) quantum object sometimes known as M-theory. How can this be? What do we know about M-theory?

Pre-requisites and co-requisites

Reading material

• Dualities of Fields and Strings by Joe Polchinski.
• Duality in Quantum Field Theory (and String Theory) by Luis Alvarez-Gaumé and Frederic Zamora.