Strong-weak Chern-Simons-matter dualities from a lattice construction

• Published in: The journal of high energy physics Vol. 2018; no. 8; pp. 1 - 35
• Main Authors: Chen, Jing-Yuan, Zimet, Max
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-08-2018; Springer Nature B.V; SpringerOpen
• Subjects: Chern-Simons Theories; Classical and Quantum Gravitation; Duality in Gauge Field Theories; Elementary Particles; Fermions; Field theory; High energy physics; Lattice Quantum Field Theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; Solid phases; String Theory; Duality in Gauge Field Theories; Lattice Quantum Field Theory; Chern-Simons Theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2018)015

A
bstract
We provide a lattice demonstration of (2+1)-dimensional field theory dualities relating free Dirac or Majorana fermions to strongly-interacting bosonic Chern-Simons-matter theories. Specifically, we prove the recent conjecture that U(
N
) level-1 with
N
f
gauged complex Wilson-Fisher scalars (where 1 ≤
N
f
≤
N
) is dual to
N
f
Dirac fermions, as well as the analogous conjecture relating SO(
N
) theories with real Wilson-Fisher scalars to Majorana fermions for 1 ≤
N
f
≤
N
− 2. Furthermore, we discover new dualities that allow us to explain the interesting phase structure of the SO(
N
) theories with
N
− 1 and
N
scalars, for all
N
≥ 2.