M5-branes, toric diagrams and gauge theory duality

Abstract

In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.

58 pages, 17 figures; v2: minor corrections, references added

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Cited by in corpus (72)

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• A new 5d description of 6d D-type minimal conformal matter
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• Quiver W-algebras
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• Dualities and 5-brane webs for 5d rank 2 SCFTs
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• Duality and enhancement of symmetry in 5d gauge theories
• Tao Probing the End of the World
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• Brane webs, $5d$ gauge theories and $6d$ $\mathcal{N}$$=(1,0)$ SCFT's
• (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
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• Equivalence of several descriptions for 6d SCFT
• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• Quiver elliptic W-algebras
• Decomposing Nekrasov Decomposition
• Holomorphic blocks and the 5d AGT correspondence
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• 5d $E_n$ Seiberg-Witten curve via toric-like diagram
• A slow review of the AGT correspondence
• Bootstrapping BPS spectra of 5d/6d field theories
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
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• An elliptic Virasoro symmetry in 6d
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Higgsed network calculus
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• Compactifications of 5d SCFTs with a twist
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• Exact Deconstruction of the 6D (2,0) Theory
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• 3d Mirror Symmetry from S-duality
• Fiber-base duality from the algebraic perspective
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Non-perturbative studies of N=2 conformal quiver gauge theories
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• Partition functions of web diagrams with an O7${}^{-}$-plane
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• On complete solution of the quantum Dell system
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Fibre-base duality of 5d KK theories
• Bootstrapping the $S^5$ partition function
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
• Cluster integrable systems and spin chains
• On generalized Macdonald polynomials
• The Condensate from Torus Knots
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Modular properties of 6d (DELL) systems
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• $DE$-type little strings from glued brane webs
• Effective Gravitational Couplings of Kaluza-Klein Gauge Theories
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras