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3d $\mathcal{N}=2$ theories and plumbing graphs: adding matter, gauging, and new dualities
High Energy Physics - Theory · Submitted 26 Feb 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that the content of such theories can be encoded in graphs, which generalize plumbing graphs, and various operations in these theories can be represented in terms of transformations of such graphs.
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The abstract, sentence by sentence
Recently, a large class of 3d $\mathcal{N} = 2$ gauge theories with mixed Chern-Simons levels, corresponding to plumbing 3-manifolds, has been identified. In this paper we generalize these theories by including in their content chiral multiples, and analyze their properties. We find that the content of such theories can be encoded in graphs, which generalize plumbing graphs, and various operations in these theories can be represented in terms of transformations of such graphs. The operations in question include gauging global symmetries, integrating out gauge nodes, which for theories without chiral multiplets corresponds to Kirby moves, and ST-transformations that involve chiral multiplets. The dualities such as mirror triality and SQED-XYZ duality can be also represented in terms of graphs, and enable us to find many new dual theories by gauging global symmetries. In particular, we find that gauged SQED-XYZ duality leads to other dualities, which take the same form as operations of linking and unlinking discussed in the context of knots-quivers correspondence. We also find that the superpotential can be encoded in an interesting class of triangle graphs that satisfy certain consistency conditions, we discuss decoupling and Higgsing of chiral multiplets, as well as interpretation of various phenomena in terms of brane webs.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently, a large class of 3d $\mathcal{N} = 2$ gauge theories with mixed Chern-Simons levels, corresponding to plumbing 3-manifolds, has been identified. | background 1.00 | 0.06 | 0.03 | asserted 1.00 |
| s1 | In this paper we generalize these theories by including in their content chiral multiples, and analyze their properties. | contribution 1.00 | 0.88 | 0.08 | asserted 0.94 |
| s2 | We find that the content of such theories can be encoded in graphs, which generalize plumbing graphs, and various operations in these theories can be represented in terms of transformations of such graphs. | contribution 0.50 | 0.94 | 0.34 | asserted 1.00 |
| s3 | The operations in question include gauging global symmetries, integrating out gauge nodes, which for theories without chiral multiplets corresponds to Kirby moves, and ST-transformations that involve chiral multiplets. | contribution 0.54 | 0.75 | 0.11 | asserted 0.99 |
| s4 | The dualities such as mirror triality and SQED-XYZ duality can be also represented in terms of graphs, and enable us to find many new dual theories by gauging global symmetries. | result 0.67 | 0.85 | 0.26 | asserted 0.98 |
| s5 | In particular, we find that gauged SQED-XYZ duality leads to other dualities, which take the same form as operations of linking and unlinking discussed in the context of knots-quivers correspondence. | result 0.99 | 0.95 | 0.16 | asserted 1.00 |
| s6 | We also find that the superpotential can be encoded in an interesting class of triangle graphs that satisfy certain consistency conditions, we discuss decoupling and Higgsing of chiral multiplets, as well as interpretation of various phenomena in terms of brane webs. | result 0.60 | 0.95 | 0.11 | asserted 1.00 |
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The paper
Original abstract
Recently, a large class of 3d $\mathcal{N} = 2$ gauge theories with mixed Chern-Simons levels, corresponding to plumbing 3-manifolds, has been identified. In this paper we generalize these theories by including in their content chiral multiples, and analyze their properties. We find that the content of such theories can be encoded in graphs, which generalize plumbing graphs, and various operations in these theories can be represented in terms of transformations of such graphs. The operations in question include gauging global symmetries, integrating out gauge nodes, which for theories without chiral multiplets corresponds to Kirby moves, and ST-transformations that involve chiral multiplets. The dualities such as mirror triality and SQED-XYZ duality can be also represented in terms of graphs, and enable us to find many new dual theories by gauging global symmetries. In particular, we find that gauged SQED-XYZ duality leads to other dualities, which take the same form as operations of linking and unlinking discussed in the context of knots-quivers correspondence. We also find that the superpotential can be encoded in an interesting class of triangle graphs that satisfy certain consistency conditions, we discuss decoupling and Higgsing of chiral multiplets, as well as interpretation of various phenomena in terms of brane webs.
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How the literature uses it
2 arXiv papers cite this in 22 sentences
Papers citing it · 19 sentences without a confident label
Uses its data or values 1 paper
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We copy the results from [ref] in below: [equation] which encode the same cubic superpotential $=XYZ$.
Fusions and Dualities for 3d Theories $T[M_3]$ · Superpotential triangles · 0.91
Cites it as support 1 paper
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This is confirmed by sphere partition function computations for the mirror duality in [ref] that the matter in the dual theory $∙_±1-$ is almost massless up to a quantum shift $q^*=e^i * ϵ$, and the mass parameter of $$ becomes the FI parameter in the dual theory $∙_+1-$.
Kirby Moves for 3d Gauge Theories · $ST$-moves as Rolfsen's surgery twist · 0.98
Cites it as background 1 paper
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After this gauging, a new gauge group is generated; see [ref] for more examples and explanation.
Fusions and Dualities for 3d Theories $T[M_3]$ · Gauge topological symmetries · 0.84
What it cites · 70 sentences without a confident label
Compares with 4 papers
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In particular, for $k=-3/2$ we obtain a mirror pair found in [ref] , with the following matrix of levels [equation] By comparing its triangle graph with $ST$-moved graphs for a bifundamental matter in [ref], we see that this triangle encodes a bifundamental multiplet.
Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories · Partially symmetric · 0.87
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This phenomenon is similar to what happens when Higging a bifundamental hypermultiplet in 5d brane webs, in which the Higgsing is interpreted as lifting a D5-brane to infinity and hence the rank of the gauge group also reduces by one, see e.g. [ref] .
Vortex Counting and Lagrangian 3-manifolds · Higgsing · 0.95
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This phenomenon is similar to what happens when Higging a bifundamental hypermultiplet in 5d brane webs, in which the Higgsing is interpreted as lifting a D5-brane to infinity and hence the rank of the gauge group also reduces by one, see e.g. [ref] .
Refined open topological strings revisited · Higgsing · 0.95
Cites as background 82 papers
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The 3d-3d correspondence was initiated among others in [ref] , where one class of 3d $=2$ theories was constructed by wrapping M5-branes on hyperbolic three-manifolds.
Gauge Theories Labelled by Three-Manifolds · 3d $𝒩=2$ theories and Kirby moves · 1.00
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These quivers also capture the content of 3d $𝒩=2$ theories corresponding to knots; each quiver node represents a chiral multiplet as well as an abelian gauge field, and the quiver matrix is interpreted as a matrix of mixed Chern-Simons levels, for details see [ref] .
BPS states, knots and quivers · Introduction · 0.85
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These quivers also capture the content of 3d $𝒩=2$ theories corresponding to knots; each quiver node represents a chiral multiplet as well as an abelian gauge field, and the quiver matrix is interpreted as a matrix of mixed Chern-Simons levels, for details see [ref] .
Branches, quivers, and ideals for knot complements · Introduction · 0.85
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