Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver

Abstract

Reflection states are introduced in the vertical and horizontal modules of the Ding-Iohara-Miki (DIM) algebra (quantum toroidal ${\mathfrak{gl}}_1$). Webs of DIM representations are in correspondence with $(p,q)$-web diagrams of type IIB string theory, under the identification of the algebraic intertwiner of Awata, Feigin and Shiraishi with the refined topological vertex. Extending the correspondence to the vertical reflection states, it is possible to engineer the $\mathcal{N}=1$ quiver gauge theory of D-type (with unitary gauge groups). In this way, the Nekrasov instanton partition function is reproduced from the evaluation of expectation values of intertwiners. This computation leads to the identification of the vertical reflection state with the orientifold plane of string theory. We also provide a translation of this construction in the Iqbal-Kozcaz-Vafa refined topological vertex formalism.

arXiv comment27 pages, 11 figures. Details of translation in terms of IKV refined topological vertex added in the second version

References in corpus (27)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Topological Vertex
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• The Refined Topological Vertex
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Refined Topological Vertex and Instanton Counting
• Small Instantons, Little Strings and Free Fermions
• The affine Yangian of ${\mathfrak{gl}}_1$ revisited
• A commutative algebra on degenerate CP^1 and Macdonald polynomials
• Quantum Algebraic Approach to Refined Topological Vertex
• Issues on Orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry
• Ding-Iohara-Miki symmetry of network matrix models
• Heisenberg action in the equivariant K-theory of Hilbert schemes via Shuffle Algebra
• Explicit examples of DIM constraints for network matrix models
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations
• D_n Quivers From Branes
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• More on 5d descriptions of 6d SCFTs
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Line defects and 5d instanton partition functions
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Topological vertex formalism with O5-plane

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• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
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• Mixed network calculus
• An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Refined topological vertex with ON-planes
• ABCD of qq-characters
• Gauge origami and quiver W-algebras
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• $DE$-type little strings from glued brane webs
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra
• Seiberg-Witten period relations in Omega background
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• Quantum $W_{1+\infty }$ subalgebras of BCD type and symmetric polynomials
• Intertwining operator and integrable hierarchies from topological strings