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Gauging and Decoupling in 3d $\mathcal{N}=2$ dualities
High Energy Physics - Theory · Submitted 7 Mar 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim One interesting feature of 3d $\mathcal{N}=2$ theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR.
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One interesting feature of 3d $\mathcal{N}=2$ theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR. The details of such decoupling, however, depends very delicately on the gauge group and matter content of the theory. We here systematically study the IR behavior of 3d $\mathcal{N}=2$ SQCD with $N_f$ flavors, for gauge groups $\mathrm{SU}(N_c), \mathrm{USp}(2N_c)$ and $\mathrm{SO}(N_c)$. We apply a combination of analytical and numerical methods, both to small values of $N_c, N_f$ and also to the Veneziano limit, where $N_c$ and $N_f$ are taken to be large with their ratio $N_f/N_c$ fixed. We highlight the role of the monopole operators and the interplay with Aharony-type dualities. We also discuss the effect of gauging continuous as well as discrete flavor symmetries, and the implications of our analysis to the classification of $1/4$--BPS co-dimension 2 defects of 6d $(2,0)$ theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | One interesting feature of 3d $\mathcal{N}=2$ theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR. | background 1.00 | 0.06 | 0.15 | asserted 0.99 |
| s1 | The details of such decoupling, however, depends very delicately on the gauge group and matter content of the theory. | background 0.52 | 0.06 | 0.04 | asserted 1.00 |
| s2 | We here systematically study the IR behavior of 3d $\mathcal{N}=2$ SQCD with $N_f$ flavors, for gauge groups $\mathrm{SU}(N_c), \mathrm{USp}(2N_c)$ and $\mathrm{SO}(N_c)$. | contribution 1.00 | 0.94 | 0.05 | asserted 0.93 |
| s3 | We apply a combination of analytical and numerical methods, both to small values of $N_c, N_f$ and also to the Veneziano limit, where $N_c$ and $N_f$ are taken to be large with their ratio $N_f/N_c$ fixed. | method 0.98 | 0.95 | 0.04 | asserted 0.96 |
| s4 | We highlight the role of the monopole operators and the interplay with Aharony-type dualities. | contribution 0.92 | 0.74 | 0.09 | asserted 0.96 |
| s5 | We also discuss the effect of gauging continuous as well as discrete flavor symmetries, and the implications of our analysis to the classification of $1/4$--BPS co-dimension 2 defects of 6d $(2,0)$ theories. | contribution 0.76 | 0.76 | 0.11 | asserted 0.88 |
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Original abstract
One interesting feature of 3d $\mathcal{N}=2$ theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR. The details of such decoupling, however, depends very delicately on the gauge group and matter content of the theory. We here systematically study the IR behavior of 3d $\mathcal{N}=2$ SQCD with $N_f$ flavors, for gauge groups $\mathrm{SU}(N_c), \mathrm{USp}(2N_c)$ and $\mathrm{SO}(N_c)$. We apply a combination of analytical and numerical methods, both to small values of $N_c, N_f$ and also to the Veneziano limit, where $N_c$ and $N_f$ are taken to be large with their ratio $N_f/N_c$ fixed. We highlight the role of the monopole operators and the interplay with Aharony-type dualities. We also discuss the effect of gauging continuous as well as discrete flavor symmetries, and the implications of our analysis to the classification of $1/4$--BPS co-dimension 2 defects of 6d $(2,0)$ theories.
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How the literature uses it
2 arXiv papers cite this in 4 sentences
What it cites · 65 sentences without a confident label
Uses the method or tool of 8 papers
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To analyze monopole decoupling in the Veneziano limit, we adopt techniques of [ref] (see also [ref] ), which gives the scaling dimension $Δ_Q$ of the quarks/anti-quarks to be
A Crack in the Conformal Window · IR Analysis · 1.00
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To analyze monopole decoupling in the Veneziano limit, we adopt techniques of [ref] (see also [ref] ), which gives the scaling dimension $Δ_Q$ of the quarks/anti-quarks to be
Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors · IR Analysis · 1.00
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The correct IR R-symmetry can be determined with the help of the $F$-maximization [ref] , i.e. the maximization of the supersymmetric partition function on the round three-sphere $S^3$ [ref] .
Notes on SUSY Gauge Theories on Three-Sphere · Introduction and Summary · 0.97
Uses data or values from 1 paper
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In particular, in the Veneziano limit[ This is natural in the context of the holographic dual.] we have learned from [ref] that the decoupling happens at the critical value $x_c≈1.45<2$.
A Crack in the Conformal Window · Boundary Conditions of 4d N=4 SYM · 0.93
Compares with 2 papers
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This is in sharp contrast with the case of the $(N_c)$ SQCD discussed in [ref] , where region for the convergent magnetic partition function was complementary to that of the electric partition function; the overlapping region exists only for fine-tuned values of $N_c$ and $N_f$, and vanishes in the Veneziano limit.
A Crack in the Conformal Window · IR Analysis · 0.97
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We have done the $F$-maximization for several small values of $N_c$ and $N_f$.[Note that part of the entries have appeared in [ref] , which gives the critical values of $a$ consistent with ours, in the first $F$-maximization.
Evidence for Aharony duality for orthogonal gauge groups · IR Analysis · 0.97
Cites as background 3 papers
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In 3d $𝒩=4$ theories there is a simple formula for the scaling dimensions of the monopole operators [ref] , which lead to the good/ugly/bad classifications of 3d $𝒩=4$ theories [ref] .
S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory · Introduction and Summary · 0.88
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In this Appendix we briefly summarize the case of the $(N_c)$ gauge group [ref] .
A Crack in the Conformal Window · U(Nc) SQCD · 0.87
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Such quiver gauge theories naturally arise in string theory (see e.g [ref] and references therein), and (as we will discuss later in the next section) for example in the compactifications of M5-branes.
Brane Tilings and Their Applications · Gauging and Quiver Gauge Theories · 0.92
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