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N=1 Duality in the Chiral Limit from N=2 Duality
High Energy Physics - Theory · Submitted 24 Mar 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the 't Hooft matching conditions in the chiral limit require the Seiberg neutral meson field M from this sector to become light.
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The abstract, sentence by sentence
We study a deformation of N=2 supersymmetric QCD with U(N) gauge group and N_f quark flavors induced by the mass term \mu for the adjoint matter which breaks supersymmetry down to N=1 QCD. Recently this deformation was shown to lead to a weakly coupled dual theory only in two particular sets of vacua: the r=N vacuum and the so-called zero vacua which can be found at r< N_f-N, where r is the number of condensed quarks. For small quark masses and intermediate values of \mu the gauge group of the dual theory is U(N_f-N)\times U(1)^{2N-N_f} where the Abelian sector is heavy and can be integrated out. However, at larger values of \mu the Abelian sector enters the strong coupling regime. We show that the 't Hooft matching conditions in the chiral limit require the Seiberg neutral meson field M from this sector to become light. In the r=N vacuum M is constructed of a monopole and antimonopole connected by a confining magnetic strings while in the zero vacua it is built of a quark and antiquark connected by a confining electric strings.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study a deformation of N=2 supersymmetric QCD with U(N) gauge group and N_f quark flavors induced by the mass term \mu for the adjoint matter which breaks supersymmetry down to N=1 QCD. | contribution 0.70 | 0.72 | 0.04 | asserted 0.98 |
| s1 | Recently this deformation was shown to lead to a weakly coupled dual theory only in two particular sets of vacua: the r=N vacuum and the so-called zero vacua which can be found at r< N_f-N, where r is the number of condensed quarks. | background 0.96 | 0.07 | 0.09 | asserted 1.00 |
| s2 | For small quark masses and intermediate values of \mu the gauge group of the dual theory is U(N_f-N)\times U(1)^{2N-N_f} where the Abelian sector is heavy and can be integrated out. | result 0.50 | 0.31 | 0.08 | asserted 1.00 |
| s3 | However, at larger values of \mu the Abelian sector enters the strong coupling regime. | background 0.53 | 0.23 | 0.04 | asserted 1.00 |
| s4 | We show that the 't Hooft matching conditions in the chiral limit require the Seiberg neutral meson field M from this sector to become light. | result 0.85 | 0.89 | 0.58 | asserted 1.00 |
| s5 | In the r=N vacuum M is constructed of a monopole and antimonopole connected by a confining magnetic strings while in the zero vacua it is built of a quark and antiquark connected by a confining electric strings. | result 0.87 | 0.83 | 0.27 | asserted 1.00 |
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The paper
Original abstract
We study a deformation of N=2 supersymmetric QCD with U(N) gauge group and N_f quark flavors induced by the mass term \mu for the adjoint matter which breaks supersymmetry down to N=1 QCD. Recently this deformation was shown to lead to a weakly coupled dual theory only in two particular sets of vacua: the r=N vacuum and the so-called zero vacua which can be found at r< N_f-N, where r is the number of condensed quarks. For small quark masses and intermediate values of \mu the gauge group of the dual theory is U(N_f-N)\times U(1)^{2N-N_f} where the Abelian sector is heavy and can be integrated out. However, at larger values of \mu the Abelian sector enters the strong coupling regime. We show that the 't Hooft matching conditions in the chiral limit require the Seiberg neutral meson field M from this sector to become light. In the r=N vacuum M is constructed of a monopole and antimonopole connected by a confining magnetic strings while in the zero vacua it is built of a quark and antiquark connected by a confining electric strings.
Human review
How the literature uses it
4 arXiv papers cite this in 35 sentences
Papers citing it · 21 sentences without a confident label
Contests it 2 papers
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Unfortunately, it was overlooked in [ref] that, in distinction with their example with $U(N_c=3), N_F=5, =2$ in [ref] with the trivial $Z_2N_c-N_F=1$ symmetry giving no restrictions on the form of $⟨X⟩$, the appearance e.g. in the superpotential at $μ∼$ of mass terms of original $SU()$ quarks like $∼Tr (QQ)_$ or terms like $∼Tr (X^2_SU())$ for scalars is forbidden in vacua with the non-trivial unbroken $Z_2N_c-N_F≥2$ symmetry, independently of whether these terms originated directly from $⟨X⟩$ or from unrecognized "outside".
Softly broken ${\cal N}=2$ SQCD: mass spectra in vacua with unbroken $Z_{2N_c-N_F}$ symmetry · Introduction · contest 0.92
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But they changed later their mind to the opposite [ Because not $SU(N_c)$ but $U(N_c)$ group was considered in [ref] , this their statement concerns really br2 and very special vacua of $U(N_c)$, see table of contents, sections 2.2 and 6 (these are respectively zero vacua and $r=N_c$ vacua in the language of [ref] ). ] and, extrapolating freely by analogy their previous results for $r=N_c=3, N_F=5, =2$ very special vacua in [ref] (see also [ref] ) to all br2 and very special vacua, stated in [ref] that this $SU()$ group is not pure electric but dyonic.
Mass spectra in softly broken ${\cal N}=2$ SQCD · Introduction · contest 0.73
Compares with it 2 papers
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In comparison with corresponding results from recent related papers [ref] of M.
Mass spectra in softly broken ${\cal N}=2$ SQCD · Conclusions · 0.95
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In comparison with corresponding results from recent related papers [ref] of M.Shifman and A.Yung (and from a number of their previous numerous papers on this subject), our results are essentially different.
Softly broken ${\cal N}=2$ SQCD: mass spectra in vacua with unbroken $Z_{2N_c-N_F}$ symmetry · Conclusions · 0.92
Cites it as background 3 papers
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We consider in this section the vs (very special) vacua with $=, =N_c, N_c < N_F<2 N_c-1$ , $⟨S⟩_N_c=0$ ( as always, $⟨S⟩_N_c$ is the bilinear gluino condensate summed over all its colors) and the multiplicity $N_vs=C^_N_F=C^N_c_N_F$ in the $U(N_c)=SU(N_c)×U^(0)(1)$ theory, when the additional Abelian $U^(0)(1)$ with $μ_0=$ is added to the $SU(N_c)$ theory (see e.g. [ref] and references therein, these are called $r=N_c$ vacua in [ref] ).
Softly broken ${\cal N}=2$ SQCD: mass spectra in vacua with unbroken $Z_{2N_c-N_F}$ symmetry · Very special vacua with $⟨S⟩_N_c=0$ in $U(N_c)$ gauge theory · 0.82
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Dynamical scenarios in the $r<N$ vacua are considered in [ref] .
Lessons from supersymmetry: "Instead-of-Confinement" Mechanism · The $r=N$ vacuum at large $ξ$ · 0.95
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We consider in this section the vs (very special) vacua with $=, =N_c, N_c≤N_F<2 N_c-1$ , $⟨S⟩_N_c=0$ ( as usual, $⟨S⟩_N_c$ is the gluino condensate summed over all its colors) and the multiplicity $N_vs=C^_N_F=C^N_c_N_F$ in the $U(N_c)=SU(N_c)×U^(0)(1)$ theory, when the additional Abelian $U^(0)(1)$ with $μ_0=$ is added to the $SU(N_c)$ theory (see e.g. [ref] and references therein, these are called $r=N_c$ vacua in [ref] ).
Mass spectra in softly broken ${\cal N}=2$ SQCD · Very special vacua with $⟨S⟩_N_c=0$ in $U(N_c)$ gauge theory · 0.90
What it cites · 78 sentences without a confident label
Compares with 3 papers
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In much the same way as in the $r=N$ vacuum we find a perfect match [ref] .
Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2 · Intermediate $μ$ · 0.93
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We see that the dyon transformation properties are the same in both, the zero and $r=N$ vacua (see ([ref])), and coincide with those for the Seiberg dual quarks [ref] .
Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories · Large $μ$ · 0.93
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The important feature apparent in ([ref]), as compared to the squark VEVs in the original theory ([ref]), is a “vacuum leap” [ref] .
Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD · $r$ Dual theory · 0.91
Cites as support 2 papers
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It allows us to increase $μ$ and decouple the adjoint fields without violating the weak coupling condition in the dual theory [ref] .
Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD · Emergence of the $U()$ gauge group · 0.96
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Correspondingly, these vacua do not have weakly coupled dual description [ref] .
Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2 · Introduction · 0.97
Cites as background 6 papers
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where $U(1)_R$ is the nonanomalous with respect to the non-Abelian gauge bosons $R$ symmetry [ref] [The gauge group of our original theory is U$(N)$, thus it includes Abelian U(1) gauge fields. $U(1)_R$ symmetry is anomalous with respect to U(1) gauge fields.
Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories · Anomaly matching · 0.87
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In this section we consider zero vacua at intermediate and large $μ$ [ref] .
Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2 · Zero vacua · 0.88
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In this section we briefly review non-Abelian duality in the $r=N$ vacua at small $μ$ established in [ref] .
Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD · Duality in the $r=N$ vacuum at small $μ$ · 0.91
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