Duality Web on a 3D Euclidean Lattice and Manifestation of Hidden Symmetries

Abstract

We generalize our previous lattice construction of the abelian bosonization duality in $2+1$ dimensions to the entire web of dualities as well as the $N_f=2$ self-duality, via the lattice implementation of a set of modular transformations in the theory space. The microscopic construction provides explicit operator mappings, and allows the manifestation of some hidden symmetries. It also exposes certain caveats and implicit assumptions beneath the usual application of the modular transformations to generate the web of dualities. Finally, we make brief comments on the non-relativistic limit of the dualities.

arXiv comment38 pages; v2: minor changes

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• Multi-critical point and unified description of broken-symmetry phases in spin-1/2 anti-ferromagnets on a square lattice
• Phases of Flavor Broken QCD${}_3$
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities