Duality between $(2+1)d$ Quantum Critical Points

TL;DR

This paper reviews recent advances in dualities of conformally invariant quantum field theories in (2+1)d, highlighting their significance for understanding quantum critical points and related condensed matter phenomena.

Contribution

It provides a pedagogical overview of recent dualities in (2+1)d quantum field theories and their implications for condensed matter physics.

Findings

Enhanced understanding of quantum critical points through dualities

Connections between dualities and topological insulators

Insights into Landau level physics from dual descriptions

Abstract

Duality refers to two equivalent descriptions of the same theory from different points of view. Recently there has been tremendous progress in formulating and understanding possible dualities of quantum many body theories in $2+1$-spacetime dimensions. Of particular interest are dualities that describe conformally invariant quantum field theories in $(2+1)d$. These arise as descriptions of quantum critical points in condensed matter physics. The appreciation of the possible dual descriptions of such theories has greatly enhanced our understanding of some challenging questions about such quantum critical points. Perhaps surprisingly the same dualities also underlie recent progress in our understanding of other problems such as the half-filled Landau level and correlated surface states of topological insulators. Here we provide a pedagogical review of these recent developments from a point of view geared toward condensed matter physics.