Description

Quantum physics is one of the major discoveries of modern physics. The framework of perturbative quantum field theory is central to our understanding of weakly interacting systems. However, the description of strongly coupled systems is a challenging task since the perturbative techniques cannot be used to study such systems. In spite of this difficulty, there exists a set of quantum field theory for which the symmetry is enhanced from the Poincare symmetry to a larger symmetry known as conformal symmetry. These are known as Conformal Field theories (CFTs). These extra symmetries play an important role in understanding the dynamics of strongly coupled systems. CFTs look the same at all energy scales and they appear in different branches of physics. They describe the universal physics of critical points e.g. the second order phase transitions in fluids, magnets.

The aim of this project is to understand critical phenomena using the idea of conformal field theory in higher dimensional space-time. The project will begin by focusing on the basic symmetries of CFTs. Then a framework will be developed to compute the critical exponents using CFT techniques. The goal of this project is to understand how conformal symmetry can be a powerful tool to unravel the salient features of critical systems at the phase transition.

Prerequisites

1. Special Relativity and Electromagnetism II (or equivalent)
2. Mathematical Physics II (or equivalent)

Corequisites

1. Geometry of Mathematical Physics III
2. Quantum Mechanics III/li>

References

1. https://arxiv.org/abs/1601.05000
2. Scaling and Renormalization in Statistical Physics, John Cardy
3. https://arxiv.org/abs/1505.00963