Topological strings and 5d T_N partition functions

Abstract

We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds. The theories include certain non-Lagrangian theories such as the T_N theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T_3 theory as well as Sp(1) gauge theories with N_f = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the T_N theory. We compute the partition function of the E_7 theory via this prescription, and find the E_7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to non-toric web diagrams.

79 pages, 27 figures; v2: minor improvements, references added

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Cited by in corpus (75)

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• Three dimensional canonical singularity and five dimensional N=1 SCFT
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
• Brane webs and $O5$-planes
• A new 5d description of 6d D-type minimal conformal matter
• Fiber-Base Duality and Global Symmetry Enhancement
• Trifectas for $T_N$ in 5d
• Instanton Operators and the Higgs Branch at Infinite Coupling
• Lifting 4d dualities to 5d
• 6d SCFTs, 5d Dualities and Tao Web Diagrams
• Duality and enhancement of symmetry in 5d gauge theories
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• Tao Probing the End of the World
• Line defects and 5d instanton partition functions
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Exact Bremsstrahlung and Effective Couplings
• Entanglement entropy vs. free energy in IIB supergravity duals for 5d SCFTs
• Magnetic Quivers from Brane Webs with O5 Planes
• Mass-deformed $T_N$ as a linear quiver
• Duality walls and defects in 5d N=1 theories
• Equivalence of several descriptions for 6d SCFT
• Rank-3 antisymmetric matter on 5-brane webs
• Exact partition functions of Higgsed 5d $T_N$ theories
• 5d $E_n$ Seiberg-Witten curve via toric-like diagram
• A slow review of the AGT correspondence
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• Bootstrapping BPS spectra of 5d/6d field theories
• Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers
• Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
• 6d $\mathcal{N}=(1,0)$ theories on $S^1/T^2$ and class S theories: part II
• Topological vertex formalism with O5-plane
• 5d fixed points from brane webs and O7-planes
• On AGT-W Conjecture and q-Deformed W-Algebra
• Wilson loops in 5d $\mathcal{N}=1$ theories and S-duality
• 6d strings and exceptional instantons
• Exact Deconstruction of the 6D (2,0) Theory
• Notes on Enhancement of Flavor Symmetry and 5d Superconformal Index
• General instanton counting and 5d SCFT
• More on topological vertex formalism for 5-brane webs with O5-plane
• Indices for 6 dimensional superconformal field theories
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Brane webs in the presence of an $O{5}^{-}$-plane and 4d class S theories of type D
• An Index for Ray Operators in 5d $E_n$ SCFTs
• Little strings on $D_n$ orbifolds
• Partition functions of web diagrams with an O7${}^{-}$-plane
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• Refined topological vertex with ON-planes
• Topological strings and Wilson loops
• 6d/5d exceptional gauge theories from web diagrams
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Topological vertex for Higgsed 5d $T_N$ theories
• Trinion Conformal Blocks from Topological strings
• ABCD of 't Hooft operators
• Surface Operators from M-strings
• Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories
• S-foldings of 5d SCFTs
• Refined topological vertex for a 5D $Sp(N)$ gauge theory with antisymmetric matter
• Thermodynamic limit of the Nekrasov-type formula for E-string theory
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• Geometric transition in Non-perturbative Topological string
• The Enhancement of Supersymmetry in M-strings
• Surface defects and instanton partition functions
• ADHM Wilson line defect indices
• Exotic Brane Junctions from F-theory
• Refined open topological strings revisited
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• Towards a gauge theory interpretation of the real topological string
• Intertwining operator and integrable hierarchies from topological strings