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.

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

References in corpus (5)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Refined Topological Vertex
• Small Instantons, Little Strings and Free Fermions
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations

Cited by in corpus (9)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• 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
• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• $DE$-type little strings from glued brane webs
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• O-vertex, O7${}^{+}$-plane, and Topological Vertex