ABCD of qq-characters

Abstract

The qq-characters are powerful tools to reveal symmetries and integrabilities of Seiberg-Witten theories. The goal of this paper is to provide analytic expressions of qq-characters based on Young diagrams in 5d $\mathcal{N}=1$ pure Yang-Mills theories with BCD-type gauge groups, by focusing on the unrefined limit. Using these expressions, we investigate the relationships among qq-characters of classical gauge groups. For SO(n) gauge groups, we construct a quantum-toroidal-like algebra via the Ward-identity approach, which allows us to derive the qq-characters.

arXiv comment27+18 pages; Mathematica file attached; explanations added in v2

References in corpus (55)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Integrability and Seiberg-Witten Exact Solution
• Integrable systems and supersymmetric gauge theory
• Elliptic genera of 2d N=2 gauge theories
• Holographic Wilson Loops
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• ABCD of instantons
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• N=2 Supersymmetric Gauge Theories, Branes and Orientifolds
• The Holographic Dual of AdS3 x S3 x S3 x S1
• Quantum Algebraic Approach to Refined Topological Vertex
• The Moduli Space and Monodromies of N=2 Supersymmetric \(SO(2r+1) \) Yang-Mills Theory
• M Theory And Seiberg-Witten Curves: Orthogonal and Symplectic Groups
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations
• Discrete theta and the 5d superconformal index
• Quiver W-algebras
• The Effective Prepotential of N=2 Supersymmetric SO(N_c) and Sp(N_c) Gauge Theories
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Line defects and 5d instanton partition functions
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Quiver elliptic W-algebras
• ADHM Revisited: Instantons and Wilson Lines
• Riemann-Hilbert correspondence and blown up surface defects
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• 5d/6d Wilson loops from blowups
• More on topological vertex formalism for 5-brane webs with O5-plane
• Instanton counting and O-vertex
• On the Jeffrey-Kirwan residue of BCD-instantons
• On the Quantization of Seiberg-Witten Geometry
• An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Instantons to the people: the power of one-form symmetries
• Elliptic Quantum Curves of 6d SO(N) theories
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
• Recursive Method for Nekrasov partition function for classical Lie groups
• Refined topological vertex with ON-planes
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• 6d/5d exceptional gauge theories from web diagrams
• Topological Vertex/anti-Vertex and Supergroup Gauge Theory
• Integrable structure of $\text{BCD}$ conformal field theory and boundary Bethe ansatz for affine Yangian
• A note on S-dual basis in free fermion system
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• Instantons on Young diagrams with matters
• Quantum Geometry and $\theta$-Angle in Five-Dimensional Super Yang-Mills
• Double quantization of Seiberg-Witten geometry and W-algebras

Cited by in corpus (8)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Defects and type D relativistic Toda lattice for some 5d gauge theories
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• New dimer integrable systems and defects in five dimensional gauge theory
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations