Bootstrapping the $S^5$ partition function

Abstract

We consider $U(N)$ SQCD on $S^5$ and propose a Higgs branch-like expression for its partition function. We support the result by arguing that the knowledge of certain BPS codimension 2 and 4 defects arising from Higgsing is enough to reconstruct the bulk partition function, and that the defect partition functions satisfy a set of non-perturbative Schwinger-Dyson equations. We show that the result is consistent with, and naturally come from, the BPS/CFT perspective. In this language, the defect partition functions are identified with free boson correlators of the $q$-Virasoro modular triple, and the constraint equations with Ward identities satisfied by the corresponding Dotsenko-Fateev $q$-conformal blocks, providing a natural basis to expand the $S^5$ partition function.

arXiv comment15 pages; note prepared for Proceedings of the XXth International Seminar "Quarks-2018"

References in corpus (66)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• SUSY Gauge Theories on Squashed Three-Spheres
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Branes, Superpotentials and Superconformal Fixed Points
• Integrating Over Higgs Branches
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• D-particle bound states and generalized instantons
• Localization techniques in quantum field theories
• Exact Results in D=2 Supersymmetric Gauge Theories
• Integrability and Matrix Models
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Bootstrapping the superconformal index with surface defects
• Issues in Topological Gauge Theory
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• Supersymmetric Gauge Theories on the Five-Sphere
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Factorisation of N = 2 theories on the squashed 3-sphere
• Seiberg-Witten Theories on Ellipsoids
• Twisted supersymmetric 5D Yang-Mills theory and contact geometry
• Seiberg-Witten Theory and Random Partitions
• Proving AGT conjecture as HS duality: extension to five dimensions
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• Higgs branch localization in three dimensions
• Ding-Iohara-Miki symmetry of network matrix models
• Explicit examples of DIM constraints for network matrix models
• Instantons on the 5-sphere and M5-branes
• M5-branes, toric diagrams and gauge theory duality
• Deformations of W-algebras associated to simple Lie algebras
• Perturbative partition function for a squashed S^5
• Quiver W-algebras
• Vertices, Vortices & Interacting Surface Operators
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• M2-brane surface operators and gauge theory dualities in Toda
• Higgs branch localization of 3d N=2 theories
• Superconformal Partition Functions and Non-perturbative Topological Strings
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Testing Seiberg-Witten Solution
• Line defects and 5d instanton partition functions
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Notes on Ding-Iohara algebra and AGT conjecture
• Gauge/Liouville Triality
• The Liouville side of the Vortex
• Kernel function and quantum algebras
• Intersecting Surface Defects and Two-Dimensional CFT
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• Factorization of 5D super Yang-Mills on $Y^{p,q}$ spaces
• Gluing Nekrasov partition functions
• On elementary proof of AGT relations from six dimensions
• Holomorphic Blocks for 3d Non-abelian Partition Functions
• ADE Little String Theory on a Riemann Surface (and Triality)
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• $q$-Virasoro modular double and 3d partition functions
• Factorization of 4d N=1 superconformal index
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Ellipsoid partition function from Seiberg-Witten monopoles
• Quantum q-Langlands Correspondence
• The modular properties and the integral representations of the multiple elliptic gamma functions
• 3d Expansions of 5d Instanton Partition Functions
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index

Cited by in corpus (8)

• A slow review of the AGT correspondence
• Surface defects in holographic 5d SCFTs
• 3d Mirror Symmetry from S-duality
• An analogue of Schur functions for the plane partitions
• Intersecting Defects and Supergroup Gauge Theory
• 3d defects in 5d: RG flows and defect F-maximization
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Intersecting Surface defects and 3d Superconformal indices