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Confronting Seiberg's Duality with r Duality in N=1 Supersymmetric QCD
High Energy Physics - Theory · Submitted 18 Apr 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus, we can speak of triality.
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The abstract, sentence by sentence
Systematizing our results on r duality obtained previously we focus on comparing r duality with the generalized Seiberg duality in the r vacua of N=2 and N=1 super-Yang-Mills theories with the U(N) gauge group and N_f matter flavors (N_f>N). The number of condensed (s)quarks r is assumed to be in the interval 2N_f/3 < r \le N. To pass to N=1 we introduce an N=2-breaking deformation, a mass term \mu for the adjoint matter, eventually decoupling the adjoint matter in the limit of large \mu. If one starts from a large value of the parameter \xi\sim\mu m, where the original theory is at weak coupling, and decreases \xi one hits a a crossover transition from weak to strong coupling (here m is a typical value of the quark masses). Below this transition the original theory is described in terms of a weakly coupled infrared-free r dual theory with the U(N_f-r) gauge group and N_f light quark-like dyon flavors. Dyon condensation leads to confinement of monopoles, defying a naive expectation of quark confinement. The quarks and gauge bosons of the original theory are in an "instead-of-confinement" phase. The r and Seiberg dualities are demonstrated to coincide in the r=N vacua. In the (2/3) N_f <r<N vacua two dualities do not match. In this window Seiberg's dual is at strong coupling while our r-dual model is at weak coupling. Thus, we can speak of triality. Seiberg's dual solution at weak coupling reappears again at r<N_f-N< (1/3) N_f$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Systematizing our results on r duality obtained previously we focus on comparing r duality with the generalized Seiberg duality in the r vacua of N=2 and N=1 super-Yang-Mills theories with the U(N) gauge group and N_f matter flavors (N_f>N). | contribution 0.92 | 0.66 | 0.08 | asserted 0.68 |
| s1 | The number of condensed (s)quarks r is assumed to be in the interval 2N_f/3 < r \le N. | method 0.46 | 0.26 | 0.03 | asserted 0.93 |
| s2 | To pass to N=1 we introduce an N=2-breaking deformation, a mass term \mu for the adjoint matter, eventually decoupling the adjoint matter in the limit of large \mu. | method 0.99 | 0.80 | 0.02 | asserted 0.99 |
| s3 | If one starts from a large value of the parameter \xi\sim\mu m, where the original theory is at weak coupling, and decreases \xi one hits a a crossover transition from weak to strong coupling (here m is a typical value of the quark masses). | result 0.79 | 0.72 | 0.03 | asserted 0.99 |
| s4 | Below this transition the original theory is described in terms of a weakly coupled infrared-free r dual theory with the U(N_f-r) gauge group and N_f light quark-like dyon flavors. | result 0.96 | 0.74 | 0.12 | asserted 1.00 |
| s5 | Dyon condensation leads to confinement of monopoles, defying a naive expectation of quark confinement. | interpretation 0.52 | 0.67 | 0.08 | asserted 1.00 |
| s6 | The quarks and gauge bosons of the original theory are in an "instead-of-confinement" phase. | interpretation 0.83 | 0.67 | 0.07 | asserted 1.00 |
| s7 | The r and Seiberg dualities are demonstrated to coincide in the r=N vacua. | result 1.00 | 0.87 | 0.21 | asserted 1.00 |
| s8 | In the (2/3) N_f <r<N vacua two dualities do not match. | result 1.00 | 0.84 | 0.30 | asserted 1.00 |
| s9 | In this window Seiberg's dual is at strong coupling while our r-dual model is at weak coupling. | result 0.85 | 0.80 | 0.19 | asserted 1.00 |
| s10 | Thus, we can speak of triality. | interpretation 0.98 | 0.69 | 0.21 | hedged possibility 0.57 |
| s11 | Seiberg's dual solution at weak coupling reappears again at r<N_f-N< (1/3) N_f$. | result 1.00 | 0.73 | 0.11 | asserted 1.00 |
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The paper
Original abstract
Systematizing our results on r duality obtained previously we focus on comparing r duality with the generalized Seiberg duality in the r vacua of N=2 and N=1 super-Yang-Mills theories with the U(N) gauge group and N_f matter flavors (N_f>N). The number of condensed (s)quarks r is assumed to be in the interval 2N_f/3 < r \le N. To pass to N=1 we introduce an N=2-breaking deformation, a mass term \mu for the adjoint matter, eventually decoupling the adjoint matter in the limit of large \mu. If one starts from a large value of the parameter \xi\sim\mu m, where the original theory is at weak coupling, and decreases \xi one hits a a crossover transition from weak to strong coupling (here m is a typical value of the quark masses). Below this transition the original theory is described in terms of a weakly coupled infrared-free r dual theory with the U(N_f-r) gauge group and N_f light quark-like dyon flavors. Dyon condensation leads to confinement of monopoles, defying a naive expectation of quark confinement. The quarks and gauge bosons of the original theory are in an "instead-of-confinement" phase. The r and Seiberg dualities are demonstrated to coincide in the r=N vacua. In the (2/3) N_f <r<N vacua two dualities do not match. In this window Seiberg's dual is at strong coupling while our r-dual model is at weak coupling. Thus, we can speak of triality. Seiberg's dual solution at weak coupling reappears again at r<N_f-N< (1/3) N_f$.
Human review
References
How the literature uses it
6 arXiv papers cite this in 28 sentences
Papers citing it · 23 sentences without a confident label
Contests it 1 paper
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It was overlooked, however, that the low-energy theory in this limit enters the AD strongly coupled regime, while our task was to find a weakly coupled dual.[In [ref] it was argued that the low-energy theory stays at weak coupling near the AD points at $μ →0$ because the monopoles which become light are, in fact, confined and, therefore, do not contribute to the $β$ function.
Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2 · Preliminaries · contest 0.88
Compares with it 1 paper
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In a forthcoming publication [ref] we will compare the $r$-duality with Seiberg's duality [ref] .
r Duality and "Instead-of-Confinement" Mechanism in N=1 Supersymmetric QCD · Introduction · 0.85
Cites it as support 1 paper
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At the same time, the zero vacua were shown [ref] to be precisely the vacua which are classically seen in the generalized Seiberg dual theory [ref] .
Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2 · Chiral condensates at small quark masses · 0.97
What it cites · 71 sentences without a confident label
Builds on 2 papers
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At the same time, the original Seiberg duality (formulated in [ref] in the monopole $r=0$ vacua) can be generalized to $r$ vacua [ref] which survive in passing from to our basic model at large but finite $μ$.[ At $μ= ∞$ only the $r=0$ monopole vacua remain, while others become run-away vacua.] Further explorations of the generalized Seiberg duality were undertaken in [ref] .
Stable and Metastable Vacua in SQCD · Introduction · 0.93
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At the same time, the original Seiberg duality (formulated in [ref] in the monopole $r=0$ vacua) can be generalized to $r$ vacua [ref] which survive in passing from to our basic model at large but finite $μ$.[ At $μ= ∞$ only the $r=0$ monopole vacua remain, while others become run-away vacua.] Further explorations of the generalized Seiberg duality were undertaken in [ref] .
Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories · Introduction · 0.93
Uses the method or tool of 1 paper
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Following [ref] , we assume that the $M_A^B$ fields develop VEVs making “dual quarks” heavy and then integrate $h^lA$ out.
Lectures on Supersymmetry Breaking · The $r<N$ vacua · 0.84
Compares with 2 papers
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We show that, upon integrating out heavy mesonic $M$-fields, this superpotential coincides with our $r$-dual superpotential obtained in [ref] .
Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD · Analysis outline and main statements · 0.94
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Now we would like to compare $r$ duality we established with Seiberg's duality [ref] .
Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories · Generalized Seiberg's duality · 0.99
Cites as support 3 papers
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The “vacuum leap” ([ref]) ensures that in the $r$-vacua we have “instead-of-confinement” mechanism for quarks and gauge bosons [ref] (assuming $1/2 N_f< r≤N$).
Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD · “Instead-of-confinement” mechanism in the $r$ vacua · 0.96
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The “vacuum leap” ([ref]) ensures that in the $r$-vacua we have “instead-of-confinement” mechanism for quarks and gauge bosons [ref] (assuming $1/2 N_f< r≤N$).
r Duality and "Instead-of-Confinement" Mechanism in N=1 Supersymmetric QCD · “Instead-of-confinement” mechanism in the $r$ vacua · 0.96
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Namely, the quarks and gauge bosons of the original theory decay into monopole-antimonopole pairs on the curves of marginal stability (CMS) [ref] .
Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings · Analysis outline and main statements · 0.97
Cites as background 3 papers
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The discovery of the Seiberg duality [ref] was a major breakthrough in Yang–Mills theories at strong coupling, with far reaching consequences both in field theory and string theory.
Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories · Introduction · 1.00
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First, we briefly review the analysis carried out in [ref] .
Stable and Metastable Vacua in SQCD · Classical and quantum $r$ vacua in Seiberg's dual theory · 0.96
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For example, a somewhat similar analysis for SU$(N)$ gauge theory can be found in [ref] .
Confining vacua in SQCD, the Konishi anomaly and the Dijkgraaf-Vafa superpotential · Generalized Seiberg's duality and exact chiral rings · 0.95
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