Dirac quantum criticality and the web of dualities

TL;DR

This paper extends the web of dualities in 2+1D conformal field theories to include Dirac fermion quantum critical points, using seed dualities and gauging techniques to relate various critical phenomena.

Contribution

It introduces new dualities for Dirac fermion critical points, including monopole operator effects and connections to known quantum critical transitions.

Findings

Matched phase diagrams, symmetries, and anomalies across dualities.

Derived dualities between different quantum critical points.

Compared monopole operator scaling dimensions with large-N expansion results.

Abstract

We grow the web of dualities for conformal field theories (CFTs) in 2+1 spacetime dimensions to include quantum critical transitions of Dirac fermions. Our construction uses the seed duality, equating a free Dirac fermion with a complex boson coupled to a Chern-Simons gauge field, to express various Gross-Neveu-Yukawa (GNY) critical points of N fermions in terms of the same number of complex bosons and partner gauge fields. In some instances, monopole operators appear explicitly in the dual action, such as for the superconducting transition of a single Dirac fermion, which is a CFT with emergent supersymmetry. We match phase diagrams, symmetries and their anomalies. By further gauging certain symmetries, we derive offspring dualities. For example, starting with the duality for the regular GNY transition of 2 Dirac fermions, we arrive at the duality between a Neel-to-VBS deconfined quantum critical point and a gauged-Gross-Neveu transition. Finally, we use a large-N expansion for monopole operators, and compare with known scaling dimensions in the simplest single-flavour GNY transition.