Quantum Hall effect and field-theoretic dualities

One of the most fruitful approaches to the fractional quantum Hall effect is based on the notion of a low-energy degree of freedom called the "composite fermion." I will describe a recent development in the theory of the fractional quantum Hall effect known under the name of the "Dirac composite fermion theory." This theory, in contrast to previous attempts, preserves the particle-hole symmetry of the microscopic theory. This theory is one example of a nontrivial duality between nonsupersymmetric field theories in 2+1 dimensions. I will also discuss the predictions of the new theory. Reference: arXiv:1805.04472.