An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems

Abstract

We generalize our analysis in [arXiv:1301.1977], and show that a 5d and 6d AGT correspondence for SU(N) -- which essentially relates the relevant 5d and 6d Nekrasov instanton partition functions to the integrable representations of a q-deformed and elliptic affine W_N-algebra -- can be derived, purely physically, from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. Via an appropriate defect, we also derive a "fully-ramified" version of the 5d and 6d AGT correspondence where integrable representations of a quantum and elliptic affine SU(N)-algebra at the critical level appear on the 2d side, and argue that the relevant "fully-ramified" 5d and 6d Nekrasov instanton partition functions are simultaneous eigenfunctions of commuting operators which define relativistic and elliptized integrable systems. As an offshoot, we also obtain various mathematically novel and interesting relations involving the double loop algebra of SU(N), elliptic Macdonald operators, equivariant elliptic genus of instanton moduli space, and more.

53 pages (inclusive of essential review material from arXiv:1301.1977). Minor change in (3.22)

References in corpus (9)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Asymptotically free N=2 theories and irregular conformal blocks
• Instanton counting with a surface operator and the chain-saw quiver
• Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors
• Notes on Ding-Iohara algebra and AGT conjecture
• Kernel function and quantum algebras
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space

Cited by in corpus (29)

• Non-Lagrangian Theories from Brane Junctions
• Topological strings and 5d T_N partition functions
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Anomaly in RTT relation for DIM algebra and network matrix models
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Quiver elliptic W-algebras
• A slow review of the AGT correspondence
• Triality in Little String Theories
• An elliptic Virasoro symmetry in 6d
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• On determinant representation and integrability of Nekrasov functions
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Orthogonal Polynomials in Mathematical Physics
• Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
• q-Painleve equation from Virasoro constraints
• q-Vertex Operator from 5D Nekrasov Function
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Existence and Orthogonality of Generalized Jack Polynomials and Its $q$-Deformation
• Super-Yang-Mills theories on S4 x R
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• A stringy perspective on the quantum integrable model/gauge correspondence
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture