Holomorphic blocks and the 5d AGT correspondence

Abstract

We review the holomorphic block factorisation of partition functions of supersymmetric theories on compact manifolds in various dimensions. We then show how to interpret 3d and 5d partition functions as correlation functions with underlying symmetry given by a deformation of the Virasoro algebra.

This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

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Cited by in corpus (31)

• Localization techniques in quantum field theories
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Lectures on AdS Black Holes, Holography and Localization
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• 5d Partition Functions with A Twist
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Localization on three-dimensional manifolds
• On (q,t)-deformation of Gaussian matrix model
• Anomaly in RTT relation for DIM algebra and network matrix models
• A slow review of the AGT correspondence
• Analyticity of Nekrasov Partition Functions
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Introduction to localization in quantum field theory
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Review of localization for 5d supersymmetric gauge theories
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• Macdonald topological vertices and brane condensates
• The 5d Superconformal Index at Large $N$ and Black Holes
• A one-dimensional theory for Higgs branch operators
• SYM on Quotients of Spheres and Complex Projective Spaces
• Gluing I: Integrals and Symmetries
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
• S-duality and supersymmetry on curved manifolds
• Virasoro Constraint for Uglov Matrix Model
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models
• Schur Connections: Chord Counting, Line Operators, and Indices
• Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory