2017/09/30 by Jean-Emile Bourgine, M. Fukuda, Masayuki Fukuda +2 · 42 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Gauge theory #Instanton #Mathematical physics #Mathematics #Orientifold #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quiver #String theory #Theoretical physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep12(2017)015
published in Journal of High Energy Physics 2017(12) (Springer Nature) · 27 pages, 11 figures. Details of translation in terms of IKV refined topological vertex added in the second version
arxiv created 2017/10/17 · openalex publication_date 2017/12/01 · arxiv updated 2017/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Reflection states are introduced in the vertical and horizontal modules of the Ding-Iohara-Miki (DIM) algebra (quantum toroidal \mathfrakg\mathfrakl1 ). 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 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.