3d Abelian Dualities with Boundaries

Andreas Karch; Andrew Baumgartner; Brandon Robinson; Kyle Aitken

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3d Abelian Dualities with Boundaries

Kyle Aitken, Andrew Baumgartner, Andreas Karch, Brandon Robinson

High Energy Physics - Theory · Submitted 7 Dec 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.14 · mentions code or data availability 0.02.

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We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory.	contribution 0.78	0.92	0.83	asserted 1.00
s1	We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.	method 0.70	0.93	0.10	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.73.

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The paper

Original abstract

We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Maxwell-Chern-Simons-Matter in AdS$_3$
hep-th 2026-10 accept novelty 7.0 of 10

The authors determine phase diagrams and boundary spectra for large-N Maxwell-Chern-Simons-matter in AdS_3, finding a protected chiral current that is lifted by Higgsing.
A Web of 2d Dualities: ${\bf Z}_2$ Gauge Fields and Arf Invariants
hep-th 2019-02 accept novelty 4.0 of 10

The paper organizes known 2d dualities (Jordan-Wigner, Kramers-Wannier, bosonization, T-duality) into a single Z2-gauging web and extends it to a moduli space of spin-structure-dependent c=1 CFTs.

How the literature uses it

19 arXiv papers cite this in 39 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 15 sentences without a confident label

Builds on it 1 paper

The interplay between boundary conditions and global symmetries presents an interesting, non-trivial extension of the study in [ref] and will require a careful analysis in order to find duality-consistent boundary conditions.

Master 3d Bosonization Duality with Boundaries · Introduction · 0.94

Uses its method or tool 1 paper

As was done in [ref] , it will be useful to rewrite all BF terms as Chern-Simons terms in order to properly account for the edge theories.

Master 3d Bosonization Duality with Boundaries · Fiducial fermions · 0.97

Compares with it 2 papers

This expression should be equivalent to the time-reversed fermion, but with the understanding that in [ref] the time-reversed fermion came with an opposite sign Pauli-Villars regulator as well; our conventions for the $η$-invariant are different here.

Master 3d Bosonization Duality with Boundaries · Abelian Reduction · 0.82
Therefore we find [equation] which is exactly the value obtained in [ref] by introducing Pauli-Villars fields.

Boundary gauge and gravitational anomalies from Ward identities · U(1) anomaly computation · 0.98

Cites it as background 12 papers

In this case, one also needs to map boundary conditions under the duality – This has been studied in two-dimensions in the context of open string worldsheet ending on D-branes, and as well as in higher-dimensions in the context of particle-vortex duality of Chern-Simons-matter theories [ref] .

Fermionization of conformal boundary states · Introduction · 0.90
There is now considerable evidence that bosonic matter coupled to Chern-Simons (CS) gauge theories and fermionic matter coupled to - roughly speaking - `level-rank dual' CS gauge theories are dual to each other in three spacetime dimensions [ref] [There are two pair of conjecturally dual theories in non-supersymmetric matter coupled Chern-Simons theories.

On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter · Introduction · 0.86
This avenue included theories with various gauge groups and matter representations [ref] .

Phases of QCD$_3$ with three families of fundamental flavors · Introduction · 0.95

What it cites · 45 sentences without a confident label

Builds on 3 papers

We will show the derivation of [ref] holds in the presence of a truncated boundary and is non-anomalous for $M>0$ so long as $R=1$ and the $P_-χ_β=χ̅_βP_+=0$ boundary condition is chosen.

Exact Boson-Fermion Duality on a 3D Euclidean Lattice · Implementation · 0.99
In this section, we will build on recent work that realized the Abelian dualities in [ref] using exact techniques.

Particle-Vortex Duality from 3d Bosonization · Lattice construction · 0.87
In this section, we will build on recent work that realized the Abelian dualities in [ref] using exact techniques.

A Duality Web in 2+1 Dimensions and Condensed Matter Physics · Lattice construction · 0.87

Uses the method or tool of 1 paper

However, we can work around that by rewriting the BF term including a spin$_c$ valued connection as [ref]

Level/rank Duality and Chern-Simons-Matter Theories · Scalar-Vortex duality · 0.84

Compares with 1 paper

These conditions can be compared to those in ferm-bc and be seen to agree – albeit by construction [ref] .

On the Schroedinger functional in QCD · Boundary conditions · 1.00

Cites as background 11 papers

To begin the analysis of Abelian dualities with boundaries, we will give a brief review of the basic players and the mechanisms that relate them [ref] .

A Duality Web in 2+1 Dimensions and Condensed Matter Physics · Review of Abelian dualities · 0.99
To begin the analysis of Abelian dualities with boundaries, we will give a brief review of the basic players and the mechanisms that relate them [ref] .

Particle-Vortex Duality from 3d Bosonization · Review of Abelian dualities · 0.99
The discussion here will be largely heuristic, while more mathematically oriented treatments can be found in [ref] .

$S$-duality of $u(1)$ gauge theory with $\theta =\pi$ on non-orientable manifolds: Applications to topological insulators and superconductors · Spin Considerations · 1.00

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