Kutasov-Seiberg dualities and cyclotomic polynomials

Abstract

We classify all Kutasov-Seiberg type dualities in large $N_c$ SQCD with adjoints of rational $R$-charges. This is done by equating the superconformal index of the electric and magnetic theories: the obtained equation has a solution each time some product of cyclotomic polynomials has only positive coefficients. In this way we easily reproduce without any reference to the superpotential or the choice of the equations of motion (classical chiral ring) all the known dualities from the literature, while adding to them a new family with two adjoints with $R$ charges $\frac{2}{2k+1}$ and $\frac{2(k+1)}{2k+1}$ for all integers $k>1$. We argue that these new fixed points could be in their appropriate conformal windows and in some range of the Yukawas involved a low energy limit of the $D_{2k+2}$ fixed point. We try to clarify some issues connected to the difference between classical and quantum chiral ring of this new solution.

arXiv comment25 pages, 1 figure; some references and few clarifying comments added on finite Nc, redundancy of the solutions, properties of cyclotomic polynomials and unitarity bounds. Results unchanged. To be published in JHEP

References in corpus (24)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• An Index for 4 dimensional Super Conformal Theories
• On Renormalization Group Flows in Four Dimensions
• Conformal collider physics: Energy and charge correlations
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• The Exact Superconformal R-Symmetry Maximizes a
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The Constraints of Conformal Symmetry on RG Flows
• Asymptotic safety guaranteed
• On Duality in Supersymmetric Yang-Mills Theory
• A Comment on Duality in N=1 Supersymmetric Non -- Abelian Gauge Theories
• Chiral Rings, Singularity Theory and Electric-Magnetic Duality
• Central Charges and $U(1{)}_R$ Symmetries in $\mathcal{N}=1$ Super Yang-Mills
• Elliptic hypergeometry of supersymmetric dualities
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• RG Fixed Points and Flows in SQCD with Adjoints
• Duality in Supersymmetric SU($N_c$) Gauge Theory with Two Adjoint Chiral Superfields
• Asymptotically Safe Grand Unification
• Asymptotic safety guaranteed in supersymmetry
• Patterns of Duality in N=1 SUSY Gauge Theories
• Safe SUSY
• Chiral Rings, Anomalies and Electric-Magnetic Duality
• Remarks on the analytic structure of supersymmetric effective actions

Cited by in corpus (2)

• Webs of 3d $\mathcal{N}=2$ dualities with D-type superpotentials
• On holographic duals of certain isolated weighted Gorenstein cDV singularities