Equivalence of several descriptions for 6d SCFT

Abstract

We show that the three different looking BPS partition functions, namely the elliptic genus of the 6d $\mathcal{N}=(1,0)$ $Sp(1)$ gauge theory with $10$ flavors and a tensor multiplet, the Nekrasov partition function of the 5d $\mathcal{N}=1$ $Sp(2)$ gauge theory with $10$ flavors, and the Nekrasov partition function of the 5d $\mathcal{N}=1$ $SU(3)$ gauge theory with $10$ flavors, are all equal to each other under specific maps among gauge theory parameters. This result strongly suggests that the three gauge theories have an identical UV fixed point. Type IIB 5-brane web diagrams play an essential role to compute the $SU(3)$ Nekrasov partition function as well as establishing the maps.

arXiv commentv1: 40 pages, 13 figures, v2: published version

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Cited by in corpus (32)

• On Geometric Classification of 5d SCFTs
• Dualities and 5-brane webs for 5d rank 2 SCFTs
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Classification of 5d N=1 gauge theories
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Magnetic Quivers from Brane Webs with O5 Planes
• AdS${}_7$/CFT${}_6$ with orientifolds
• Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study
• Flavor Symmetry of 5d SCFTs, Part 2: Applications
• Rank-3 antisymmetric matter on 5-brane webs
• Blowup Equations for 6d SCFTs. I
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• Bootstrapping BPS spectra of 5d/6d field theories
• Dualities of 5d gauge theories from S-duality
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Discrete theta angle from an O5-plane
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• Topological vertex formalism with O5-plane
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Exploring the orthosymplectic zoo
• Partition functions of web diagrams with an O7${}^{-}$-plane
• Little strings on $D_n$ orbifolds
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Surface defects on E-string from 5-brane webs
• Fibre-base duality of 5d KK theories
• Topological Vertex/anti-Vertex and Supergroup Gauge Theory
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Refined open topological strings revisited
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations