Abstract
We show how particle-vortex duality in dimensions arises as part of an intricate web of relationships between different field theories. The starting point is “bosonization,” a conjectured duality that uses flux attachment to transmute the statistics of relativistic particles. From this seed, we derive many old and new dualities. These include particle-vortex duality for bosons as well as the recently discovered counterpart for fermions.
- Received 20 June 2016
DOI:https://doi.org/10.1103/PhysRevX.6.031043
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
A recent convergence of ideas in condensed matter physics—from the half-filled Landau level to topological insulators—has focused attention on dualities in -dimensional field theories. The idea of duality is that two very different-looking quantum field theories can actually describe the same physics.
A surprising, recent example of duality states that -dimensional QED with a single fermion is actually equivalent to a free fermion. A previous bosonic version of this statement has been long known and is referred to as particle-vortex duality. Here, we show that underlying both of these statements is a more basic proto-duality that converts a boson into a fermion through the attachment of flux, a process known as “bosonization.” By manipulating path integrals, we recover both the fermionic and bosonic particle-vortex dualities, together with many more.
We expect that our techniques will enable researchers to construct further dualities that will be important in both condensed matter physics and string theory.